My blog covers Zanzibar to Nairobi (see my signature)
For Zanzibar I'd recommend arriving in Dar es Salaam and booking tickets for a ferry the next day. Having met other tourists there that tried to get tickets for that day, they said it was a nightmare (and one couple even had to get help from our guide too!). In Stonetown, you can't miss out on the night markets held in the park across from the fort and House of Wonders. The food and atmosphere are brilliant. If you have more than 1 night there, there are a heap of resteraunts, Mercury's is ok and there are a couple on the other side of the tunnel from the park that have great lunch menus. Further afield, I'd recommend doing a spice tour - one where you can have fresh spices/ teas/ fruits makes it completely worth it and it's amazing to actually see the spices 'pre-spiced' and still growing. Try to have a local meal too because the cuisine is the best (ugali, stews, seafood, veggies - all yum!)
If you have more time still, head up north around Nungwi to get some beach time. Zanzibar has a number of dive sites scuba & snorkling and some great bars to drink the night away (or dance... or eat... or chill, whatever you're after). There is also a forest in the central-south region (I didn't go but if I'd had more time I would have for sure) where you can see Red Colobus Monkeys. You can get day trips from Nungwi for most activities and find cheap places to stay (we stayed in Amaan Bungalows which was next to some expensive places but much cheaper)
Hope it helps, and if you want recommendations on more of that area of Africa, I'm sure we can help or as Louise suggested, there are a heap of blogs covering it too.