Tokyo to Ashikaga Flower park - rail pass?

Hello! I will be staying at Tokyo Hyatt Regency next month for 3 days.
Do I need to buy a rail pass, and if so, which one?

Here is my rough plan:
1. Hyatt Regency to Ashikaga Flower Park on Day 1
2. Hyatt Regency to Kamakura on Day 2
3. Hyatt Regency to Tokyo National Museum on Day 3

Do I need to buy a rail pass for the 3 visits? If so, which one?

Thanks!

You can buy a Tokyo Wide Pass (3 consecutive days) for 10,000yen. If you take the Shinkansen option to Tomita via Oyama, the round trip from Tokyo is about 9500yen. If you combine that with the round trip to Kamakura (the pass is good only to Kamakura), then it may pay off. However, there are cheaper alternatives to Tomita.

http://www.japan-guide.com/e/e3850.html

You never "need" a rail pass - the question is if you save money in using one.
For your plans, definitely yes. And there is no reason not to take the shinkansen and save time if you get the Tokyo Wide Pass.

But it's too little for one full day - if you are up for it, you could include the Hitachi Seaside Park too - it'd mean about 2 hours more on the train to get there and the last part is not on a JR line so you'd need to pay 570 yen, but you'll think a part of heaven descended and landed at your feet.
http://en.hitachikaihin.jp/
And if by chance you still have time after that, on the way back go see Kairakuen in Mito - it is one of Japan's traditional Top 3 gardens.

Also for Kamakura, if you're going to put in a full day, you might go to Enoshima in too - it is a great addition. If you still have time after all that, then go see the Sankeien Garden in Yokohama.
Tokyo has numerous gardens too if you are interested. You could easily fit in one during your last day.

Thank you both for your quick responses!
That really helped me out!

I think I will just pay as I go for Ashikaga Flower Park, as I am not yet sure of my Kamakura trip.

I love the idea of including the Hitachi Seaside park! And will figure out how to do that - any suggestions for the best way to plan trip from Shinjuku to Ashikaga to Hitachi and back? Also is Sat or Sun better? probably both are equally crowded at this time, but was wondering if one day might be somewhat better than the other?

Thanks so much!!

Both parks are about 2 hours from Tokyo. If you look at the link given for Ashikaga above there is a clear section on how to get there. Likewise for Hitachnaka you can look at the website's access page and just reverse the route to get back to Tokyo. I will amend what I wrote earlier though - it will take about 200 minutes with a good connection from one park to the other, although you could shave a bit off by taking a bus from Katsuta Stn to Hitachinaka instead of the Hitachinaka Seaside Railway. Timing is important as well - you can see rail schedules and fares on www.hyperdia.com - the station nearest the Ashikaga Flower Park is Tomita and the one closest to Hitachinaka is Ajigaura. The parks open at 9AM and 9:30AM respectively, so with an early morning start seeing both is still quite doable.

If you are going to the park (especially Ashikaga) at the peak of the wisteria season, you can expect to see huge crowds there. Nemophila at Hitachinaka are also gorgeous and attract a number of people. You didn't specify if you're going during Golden Week, which is a peak travel season. If possible, a weekday would be preferable. Otherwise, choose whichever day appears to have better weather - use a weather.com or some other website for the forecast.
If you are not going to get the Tokyo Wide Pass, then you could still save money for Kamakura/Enoshima with an Enoshima-Kamakura Freepass.
http://www.odakyu.jp/english/deels/freepass/enoshima_kamakura/

Thank you so much for your help and detailed guidance!