Ticket to be purchased for an 8-day visit

I am doing my checklist for my visit in Japan as early as now to maximize my travel for 8 days. And I'm wondering if I could maximize the use of JR Pass in the following destinations or do I need to purchase another type of train pass?

Destinations:
- Kansai Intl Airport to Namba
- Namba to Universal Studios (vice versa)
- Namba to Kyoto
- Around Kyoto
- Kyoto to Hakone
- Hakone to Sanrio Puroland
- Downtown Tokyo
- Tokyo to Namba or Kansai Intl Airport

Your recommendations will be greatly appreciated. Thank you.

Non-JR Nankai lines connect KIX and Namba area.
Limousine buses from KIX arrive to Namba OCAT near JR-Namba Station.
- Minami (Namba)
http://www.japan-guide.com/e/e4001.html
On the map in "How to get there" you can check locations of stations and names of lines.

If you head to Kyoto and return to KIX within 7 consecutive days, a 7-day Japan Rail Pass is worth considering.

Namba to Universal Studios (vice versa)

There are some possible routes depending on your location in Namba.
e.g.
Osaka-Namba --(Hanshin)-- Nishikujo --transfer--
Nishi-Kujo --(JR-West: Sakurajima Line)-- Universal City.
e.g.
Namba -- (Subway: Midosuji Line) -- Umeda -- transfer--
Osaka ---(JR-West: Osaka Loop Line and Sakurajima Line)-- -- Universal City.
e.g.
Namba --(Nankai)-- Shin-Imamiya --transfer-- Shin-Imamiya --(JR-West: Osaka Loop Line)--
Nishi-Kujo --(JR-West: Sakurajima Line)-- Universal City.

Around Kyoto

Inside Kyoto City, non-JR bus / railroad lines may be more useful.
A one-way Kyoto bus card (sold at 500 yen) is good for major tourist spots around Kyoto Station.

Kyoto to Hakone

Hakone area is not served by JR. You can make a transfer between JR and Hakone Tozan Railway in Odawara.

Hakone to Sanrio Puroland

You can travel from Hakone-Yumoto via Odawara to Odakyu Tama Center fully by non-JR lines.
The three stations which are closest to Sanrio Puroland are non-JR stations.

Thank you so much for the reply..:)
So basically JR Pass would be useful during my visit to Namba, Universal Studios, Tokyo and back to KIX. But I still need to purchase another pass to visit around Kyoto and Hakone? Did I get it right? Will the pass for non-JR lines could also be purchased in a discounted price?