Nice hotel in Zanzibar!

Best beaches are in the north (Nungwi, Kendwa) and east (Matemwe, Pongwe, Paje). The east-coast beaches are a bit more picture-perfect, but not good for swimming for most of the day (shallow water, no water at low tide), while the north has deep water for swimming, but is less picturesque (no leaning palm trees) and a bit budier.

We stayed on Pemba (small island outside Zanzibar) for our honeymoon at an amazing resort... Fundu Lagoon. Would recomment it to anyone, one of the best places ever!

What is your budget?

mtoni marine on the west coast is lovely

Our budget is somewhere under 100 euros per person per night for half board, though preferably between 50-80 euros. Thanks for all the tips - keep ´em coming! We´ve read about the changing tides on the east coast and are wondering if this really is something that makes the whole eastern side of Zanzibar worth avoiding...?

With your budge you can stay at some pretty nice places.
Depending on how much time you have, you should spend a couple of days in town, followed by one or two different beach destinations. Mtoni Marine mentioned above is great if you have very limited time and want to have a bit of both (close to town, but with a bit of a beach feeling to it), but quite frankly, it is neither as atmospheric as some of the places IN town, nor is the beach there anything like the beaches north or east, so if you have the time, split it up. Just mho, of course.
Deciding between east and north is a really difficult one, as the two are very different. Ideally, do both. If that's not possible, decide which is more important to you - water sports, including swimming and a bit more place to chose from regarding meals and night life(north) or incredibly white and fine sand and a picture-perfect setting, coupled with an extremely laid back atmosphere (east). Tough one. Even after having been to both coasts literally dozens of times, I still cannot decide which one I prefer...

I've just come back from Zanzibar... fantastic accommodation at Pongwe Beach Resort - it is very relaxing and beautiful views. The tides are huge but it is great paddling and exploring. I didn't find the snorkling that great there though went out for an hour to nearer the reef - there were some nice bombies there but I'm comparing everything to the Great Barrier Reef and it's not that! Loved Pongwe Beach Resort. Avoid Chavda Hotel in StoneTown at the moment - they are renovating and working through all daylight hours every day.
have a great trip

Head up north for the nicest beaches. And don't forget to remind all those tourists you see buying 'dead' shells from locals on the beach that they are only dead because they were taken out of the water!!!!