Nairobi is a great lively city, but not for a naive first time tourist to East Africa. It’s not recommended that you walk around - day or night - with any valuables, unless you really know where you are going. If I were you, I would only use Nairobi as a transit hub, and only spend one night in the city. It has a high rate of crime and is often called Nairobbery. That’s not to say the city isn’t great, it has some great history and people - and you can have a great time there. It’s important to just keep your wits about you.
If you are spending the night in Nairobi, it’s best to always take a taxi cab even during the day. Two-midrange hotels, Hotel 680 and Hotel Boulvard, are usually recommended by other travelers. They are safe, secure and can organize your shuttle service to Moshi. The hotels are about $50 to $75 per night. There are other youth hostels in Nairobi if you are looking for a more affordable place to stay - Nairobi Backpackers, YMCA and Nairobi Youth hostel.
Here are some booking links for hotels via Bootsnall.com
http://www.bootsnall.com/hostels/re/Kenya/Nairobi+Hostels.php
Besides that, don’t let your first impression of East Africa be that of Nairobi. It’s like arriving in Detroit for your first time in America and thinking that is indicative of the rest of the America. It’s not. East Africa is magical, you just need to get out of the city and meet the locals and farmers of the countryside.
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