Yokohama in June - 1 to 2 Days from Ikebukuro

I'm interested in visiting Minato Mirai, Zoorasia, Sankeien Garden, Chinatown, Hakkeijima, and and Ramen Museum (Is the Cup Noodles Museum worth it and Kirin Beer?)
Any other recommendations for a must visit at Yokohama?
Can I do all of this is in 1 or 2 days?
Will any passes be worth getting to go around? (Or is Suica/Pasmo good enough?)
What's the best days and times to go and come back to Ikebukuro?

Any day, any time for travelling. It's a very short journey from Tokyo stations on several routes. Check which stations you want to use for your route when you get there, as there are several options.

The Landmark Tower is usually cited as the observation deck for Yokohama, but I liked the Marine Tower, a short walk from Chinatown. It is older and has a bit of character, giving you a good view of the area.

From Ikebukuro, Fukutoshin subway trains go all the way to Minato Mirai.

June 2, is Yokohama port opened anniversary.
Although not decided yet scheduled for this year, fireworks will increase probably at the district Minato Mirai.
If the weather is good.
In addition, such as the bazaar in the vicinity of Yokohama park(Koen) also be opened.
There are other events.
http://www.yokohamajapan.com/events/annual_events/annual_june/
If the time, it is recommended to 1 night.
Perhaps, after the fireworks will train is quite crowded.
If go to Kamakura and Enoshima, it might be for 2 nights.

Your destinations are roughly in three areas. So, it would be ideal to stay at the middle, minato mirai, and visit the south and the north on separate days. Then, do the minato mirai area at the end of these two days or on another day. I believe commuting to the similar directions for more than two days would be a waste of time.

Minato Mirai http://www.minatomirai21.com/
Cup Noodles Museum http://www.cupnoodles-museum.jp/
Chinatown http://www.chinatown.or.jp/

Zoorasia http://www2.zoorasia.org/
Ramen Museum http://www.raumen.co.jp/
Kirin Beer http://www.kirin.co.jp/entertainment/factory/yokohama/

Hakkeijima http://www.seaparadise.co.jp/
Sankeien Garden http://www.sankeien.or.jp/

Let's say I have a hotel already at Ikebukuro.
Should I need to stay in Yokohama as well, or can I just travel there on the days I would like to visit and come back?

If you have a hotel already then it wouldn't be a problem commuting. Ikebukuro and Yokohama are only about 35 minutes away from each other by train.

As a resident of view, Minato Mirai, Zoorasia, and Hakkeijima are full-day destinations, while Chinatown, Ramen Museum, and Sankeien Garden would be half-days. Then, already 4.5 days in total. If I assume an average traveler would do twice faster than a resident, he could do all these in marginally in two days (so, I indicate two full days or more in my previous post).

If you could do much faster or drop some, the commuting loss would not be a big problem. If not, more than one hour loss in a day could impact your strategy. Anyway, it would highly depend on your pace of travel. I suggest you to check the needed transportation time from your hotel by GoogleMaps and also opening hours of your destinations (so, I list all the web sites).
https://www.google.com/maps/dir/Ikebukuro+station/Minato+mirai/

And I agree with Luisjp, those sights are halfday plus each in scope. You'll need at least 2 days just to run through, and more like 3-4 just to see them topically. Keep in mind that you will be losing lots of time to transfers as well.

As Zoorasia would start from 930 and Hakkeijima from 900, GoogleMaps suggests the below:
D1: Ikebukuro/758-926/Zoorasia(4h)/1345-1426/Ramen Museum(2h)/1626-1700/Minato Mirai(4h)/2105-2206/Ikebukuro
D2: Ikebukuro/741-900/Hakkeijima(4h)/1312-1408/Sankkeien(2h)/1608-1637/Chinatown(2h)/1838-1932/Ikebukuro
The morning rush could be a problem. The late arrival in the first day suggests a night at Minato Mirai. In that case, you could enjoy a morning walk around Yamashita Park on the second day. How about to leave the large luggage at Ikebukuro, carry a small bag for Yokohama, and check in again at Ikebukuro.

In June, the sun rises quite early. If you do Kamakura(&Enoshima) as well, you could assign morning hours for Kamakura. Some temples should open early in the morning.
D1: Do Kamakura1, after the morning rush, do Hakkeijima & Sankeien.
D2: Do Kamakura2, similarly do Minato Mirai & Chinatown.
D3: Do Kamakura3, do Zoorasia & Ramen Museum.
For all the three days, you could commute from Ikebukuro before the morning rush starts. However, it would be more natural to stay at Kamakura for three nights in this case.

Minato Mirai http://www.minatomirai21.com/
11:00-23:00 Landmark Tower http://www.yokohama-landmark.jp/page/
10:00-18:00 Cup Noodles Museum http://www.cupnoodles-museum.jp/
Chinatown http://www.chinatown.or.jp/
10:00-22:30 Marine Tower http://marinetower.jp/

9:30-16:30 Zoorasia http://www2.zoorasia.org/
11:00-22:00: Ramen Museum http://www.raumen.co.jp/
Kirin Beer http://www.kirin.co.jp/entertainment/factory/yokohama/
11:00-22:00 SVB Yokohama http://www.springvalleybrewery.jp/yokohama/#_ga=1.105673099.945708308....
11:00-22:00 BeerPort http://www.kirin.co.jp/entertainment/factory/yokohama/restaurant/beerp...

9:00-19:00: Hakkeijima http://www.seaparadise.co.jp/
9:00-17:00 Sankeien Garden http://www.sankeien.or.jp/

Some other samples by GoogleMaps:

Stays in Yokohama(Kannai) with a fast pace:
D1: Kannai/826-921/Zoorasia(4h)/1345-1426/Ramen Museum(2h)/1626-1700/Minato Mirai(4h)/2105
D2: Kannai/816-854/Hakkeijima(4h)/1312-1408/Sankeien(2h)/1608-1637/Chinatown(2h)/1838-1932/Ikebukuro

Stays in Kamakura with a slow pace (daylight: 430-1900):
D1: Kamakura/758-854/Sankeien(3h)/1202-1255/Hakkeijima(6h)/1903-1942/Kamakura
D2: Kamakura/914-955/Minato mirai(6h)+Chinatown(3h)/1900-1939/Kamakura
D3: Kamakura/804-921/Zoorasia(6h)/1535-1617/Ramen Museum(3h)/1926-2017/Ikebukuro
Many famous temples in Kamakura start after 800. Only Hachimagu shrine opens at 500. Many hiking trails around Kamakura should be opened, though.
http://sunsetsunrisetime.com/Japan/Kamakura_12699.html

Wow, so much info, thank you so much!

I'm staying in Tokyo for 9 and a half days.
My direct place that I'm staying at is near Ikebukuro (Close to Otsuka Station actually).
I already booked an apartment for my stay.
I'm just hoping to see the most out of Yokohama that I can, while seeing the most I can out of Tokyo too.
I'm not sure if I can fit Kamakura/Enoshima into my itinerary or not.
You guys are really helpful, I appreciate everything!

(Maybe you can help me out with figuring out an itinerary)

Hey Luis, is there any way to get in contact with you?

I found a flower road somewhere between Otsuka and the Sunshine City. It should be near the Toden Arakawa Line.

Yokohama Kaikosai (Port Festival) is on Jun 1st and 2nd this year. Fireworks would be on the last day.
http://www.kaikosai.com/

Kamakura itself could fill up a full day, if you like history. At least nine passes are available to the Kamakura and Enoshima area.
http://holidaynote.com/joushaken/kamakura/

Last year, the Sanno Matsuri started on Jun 7th (Sunday).
http://www.tenkamatsuri.jp/nittei/index.html

It seems you have to wait for the schedule of the Sanno Matsuri. If they start the festival from Jun 5th, Harajuku should be on Jun 4th.

I usually make a table for AM/PM/night. Here is an example.

05.30 / / Ikebukuro / Ikebukuro
05.31 / Disney Sea / Disney Sea / Disney Sea
06.01 / Seaside Paradise / Sankeien / China Town
06.02 / MM21 / MM21 / MM21
06.03 / Zoorasia / Ramen Museum / Tokyo Dome
06.04 / Harajuku / Shibuya / Shibuya
06.05 / Sanno Matsuri / Shinjuku / Shinjuku
06.06 / Ueno / Akihabara / Tokyo City View
06.07 / Kamakura / Kamakura / Enoshima
06.08 / Asakusa / Odaiba / Ginza

05.31 is the best for Disney Sea by this site:
http://www15.plala.or.jp/gcap/disney/

Roppongi do have another one such as Tokyo Midtown, rather than TCV:
http://www.roppongihills.com/tcv/jp/