Weather for first couple weeks of December (for Honolulu - other parts of the island will vary) is an average high temperature of 82. Overnight low 67-69. Keep in mind that it isn't the temperature that gets you here - even in summer the average high is only 89 and 91 would be hotter than normal! The problem is the sun hitting you more directly. You can stand in the shade of a telephone pole and feel fine, but step out and it can wear you down. Rain in Honolulu ranges from an average daily low of 0.012 in early July to 0.104 at the start of January. So you are going fairly close to the peak of rainy season (early December is about 0.087). But as with most places, you can have a long streak of no rain or rain every day. Usually you'll get rain in light showers that come and go when you do have rain. There is more rain on the North Shore and Windward coasts because the clouds hit the mountains and a lot never reaches Honolulu.
Dole Plantation is right on the way to the North Shore, unless you take the long way up the Windward Coast. So might as well stop in. They have souvenir stuff there too and refreshments. A big maze, a little train, etc. I've only gone through their garden area and the store though. More info at:
http://www.dole-plantation.com/
Lots of beaches in Hawaii! Some don't have lifeguards though. Waikiki beaches themselves vary a lot. Different sand textures. Just east of Waikiki and across the street from the big mall is Ala Moana Beach Park. More locals will be there compared to Waikiki. Less crowded from what I've seen. But nice beach. Hanauma Bay is not just a place to snorkel. It's a nice beach too. Lots of North Shore beaches well known for surfing (Sunset Beach, Waimea Bay, etc). Behind Waimea Bay is a nice little nature area (Waimea Beach Park or something like that).
Various beaches in Haleiwa. Oh, and just east of Waimea Bay is Shark's Cove - area where rocks block a lot of the water so you can wade in easily.
Heck, when I first came here, I just drove around the island, stopping at any beach that looked interesting. But like I said, some won't have lifeguards. Oh, there is Sandy Beach just past Hanauma Bay - but it is a rather dangerous beach so I don't go in the water there.
Don't do anything dumb. For example, it seems every so often so young guy will go over to a blowhole - ignoring warning signs - and have a wave knock him into the hole and die.
You can take a bus around most of the island (it doesn't go way out the west side for example. It takes about four hours if you never get off - at least that's how long it took about 10 years ago! It's bus 52 or 55 - same bus. It just changes its number at Turtle Bay on the North Shore. They go both directions and I'm not sure which may give the best views, but I'd guess going counter-clockwise may be best since, if you sit on the right side, you should have the best ocean view.