By far, I'd recommend The Modern Honolulu for an anniversary vacation--if you're willing to spend a bit extra on accommodations. The vibe is very chic, modern and sexy with a great scene at the pool during the day. (Morimoto Waikiki is the signature restaurant, so it's a good spot to have a splashy dinner.) Plus, it's at the beginning of Waikiki, so you can get in and out quickly with a rental car. You can also walk in 10 minutes to Ala Moana Center to do some major shopping. Even if you don't decide to stay there, definitely stop by the pool bar at The Modern for a sunset drink.
If you're looking to spend a bit less but still want a more tasteful experience, there are a few boutique hotels. Try the Shoreline Hotel Waikiki (close to Royal Hawaiian Center for restaurants and shopping on Kalakaua Ave), Hotel Renew (just steps from Waikiki Beach), or Vive Hotel Waikiki. If you want some space but still want to be just a 10 min walk from Waikiki, you could try The Lotus At Diamond Head. This used to be the W Honolulu. It's right near Sans Souci Beach (aka Kaimana Beach), a very popular beach with locals. Great relaxed vibe without all the crowds.
I try to stay at condos in Honolulu because they are cheaper than hotels and provide more amenities. I use the website "Vacation Rentals By Owner" or just google Honolulu condos. I have stayed at The Banyan and the Aston Waikiki Sunset on Waikīkī Beach and Coconut Plantation and the Marriott's Ko Olina Beach Club at Ko'Olina on the other side of Ohua.
Outrigger Waikiki On the Beach - love this hotel. it has a restaurant where you cook your own steaks for dinner. it's a lot of fun and right on the beach. the have a guy that plays guitar and sings a ton of jack johnson songs.
I love the Hilton Hawaiian Village Waikiki Beach Resort. they do a canoe ride where you actually ride the waves. it's a ton of fun. kinda like a rollercoaster feel. you get the feel of surfing. I love Waikīkī Beach. i saw don ho here. he was amazing and a true legend. he also answered his phone during the show. and it wasn't a cell phone. it was a landline.
By the way, Diamond Head Crater Hike is a real highlight. the view back to waikiki is amazing. it can get a little crowded but well worth it. we took the bus, no need to rent a car if you don't have one.
Try the Sheraton Waikiki. This is an awesome hotel right on Waikiki beach. They have lounge chairs that you can put right in their infinity pool that overlooks the beach. Pure relaxation!
This is the "oldish" (but completely up to date) Waikīkī at it's 1930's best.
Make sure to check (even older) Moana Surfrider, A Westin Resort & Spa at it's (modern antique) best
Pricey to Costly, but Ian "what's his name" hotel done right.
This is the "new" Waikīkī at it's best.
But, honestly Waikīkī is so good and so friendly that sleeping in Kapiolani Regional Park (the largest and oldest public park in Hawaiʻi, located in Honolulu, Hawaiʻi on the east end of Waikīkī just beyond Kuhio Beach Park) with the homeless folks is cost free and great fun.
There are plenty of public bathrooms and showers - you can save a bundle of $$ by staying in the park
Hilton Hawaiian Village Waikiki Beach Resort is very nice. They have several different towers with different price points. It is on the beach and close to Waikiki.
All of the places Marc M recommended are great - but can be pricey! If you don't mind being one block from the ocean (rather than ON the beach), you can get a much better deal. I've stayed at Hotel Renew and would highly recommend it. It's small but very clean, modern, and only one block from the beach. I don't think it has a pool, but when you're in Hawaii you shouldn't be swimming in a pool anyways!
my favourite hotel is the Outrigger Reef
the beach is literally 20 metres away and there are usually great deals and there is an information centre in there. the town is very close and there are lots of fun and romantic things to do eg. luaus walks and amazing restaurants all for great prices. it also has a great pool