I used to live in Maunawili, right near mount olomana, which is a FANTASTIC place to see the windward side from. It is a bit of a strenuous hike, a couple hours, but well worth it. There are a number of great photo ops on the climb up as well as once you are at the top. Here is a site that mentions how to get to the trail head, you will probably have it all to yourself:http://oahuhiking.com/olomana.htm
Makapuu point has a neat lighthouse and is a much easier walk, on paved trails if you are looking for that.
If you are looking for nice beaches, Kailua State park is great, but just east of there is Lanikai beach, which is fantastic. Hanauma Bay is the main attraction for snorkeling if you have underwater gear. Of course the north shore is amazing especially when the break is happening. There is also swimming with the dolphins on the far west shore.