choose 1 or 2 (in kyoto)

I only have time to pick 1 or 2 of these options, and I don't know what is more worthwhile:
-Nijo castle
-Heian chrine
-Nara day trip/deer park
-kiyomizu temple

OR help me plan my itinerary. I will be in Kyoto for 3 days. Here is what I have so far:
day 1: kiyomizu temple, maruyama park, and then gion at night.
day 2: inari shrine, nara, pontocho at night
day 3: golden pavillion, arashiyama

I for sure want to see inari, maruyama, gion, golden pavillion, and arashiyama area, so i can't leave these out.

I don`t like nara that much. I am too afraid of those beasty deers! One time I saw a little child with dango in his hand and I thought "wow, do the parents want to kill their child???"

but the great buddha is a look worth! very impressive. but 3 hours are enough for nara, I think.

Out of the things you listed I like Kyomizu. The walk up to temple is nice with all the shops and the streets around the area are also nice to stroll along. I also like the view from the temple. Nijo castle is also interesting, but it depends if you are seeing, or have seen, other castles in Japan before. If you are, then i would choose Kiyomizu.

your itinerary looks fine:
1. Kiyomizu to Maruyama Park is a lovely half day..plenty of time for Gion
2. Inari Shrine is on the way to Nara..easily achievable in a day with a return and Pontoncho at night
3. Kinkakuji, and Ryoanji are good together, and then the electric railway to Arashiyama is easy
So no problems..BTW Gion and Pontoncho are a lovely evening: check the Lonely Planet guide to the area
Have fun...

how many hours should i budget at each location in your opinions?

I suggest Nijo Castle (Went there myself. Get the audio tour tapes) and if you can, the Kyoto imperial palace. Search this site for it. You have to reserve a day to visit. They limit attendants to avoid security risks.