Earlier this year, (namely July) I had the opportunity to rent an apartment and live in downtown Baku for five weeks. During these 5 weeks, I had the opportunity to explore Baku and the surrounding area. First off, renting an apartment was quite the task. For my trip, I had a company (FINCA Azerbaijan) rent find an apartment for me. When I arrived at the first apartment they chose for me, I was shocked at how horrible it was, how far from the center and how expensive it was (1500 USD a month). I simply told the company this would not work for me. I had to spend one day in this apartment and they found me another apartment for the same price much, much closer to the center and much nicer (two bedrooms, large kitchen, formal dining room, large living room, air conditioning, satellite etc.)
After settling the apartment issue, I was able to spend much of my time exploring Baku. In the bay that Baku is situated on, there are several companies who offer guided boat tours, these tend to be crowded, and extremely boring.
"Old Baku" is extremely interesting. The Maiden Tower standing out. It's a tower maybe 26 meters tall that was used to lay dead bodies on so that birds could pick the bones clean. Then the bones would be placed in the walls of the towers for safe keeping. Surrounding the tower are yards of ruins just laying out, no fences or anything. There are exceptional markets near the tower and on the most popular street, Nezami, where excellent silk carpets, copper products and art can be purchased.
The beaches are extremely underdeveloped. There are hardly any resorts and there aren't any decent ones. Even though the Caspian is crowded with oil platforms, the water is remarkable clean. The weather is very nice from April to September or October. Day trips can be taken to surrounding cities like Sumgayit with less populated beaches. These beaches are less populated as I said before, but still as underdeveloped.
Quick Tips:
Baku offers several restaurants that are nice according to western standards. Several of them are owned and run by ex-patriots. Use the Lonely Planet Azerbaijan book. I used several, but the Lonely Planet has the best guide to restaurants, shopping and tour location/prices.
Visit the old city. It's surrounded by a wall rumored to be 12 hundred years old. Its really quite beautiful with several extremely old buildings that match the architecture of the Maiden Tower and old wall. There are a view very nice hotels located within the walls of the old city, they are very expensive and sometimes completely booked.
If you're bored in the evening and don't have anything to do. Try loitering at the city park. It's just 3 blocks north east from Nezami. It's almost always full of families, youth and couples at night, just walking around or sitting on one of the scores of comfortable benches. The fountains down the middle are beautiful and are turned on every night.Best Way To Get Around:
The metro is inexpensive, but useless if you're staying in the center of the city. The metro is mostly used to leave the center of the city and go to the soviet block apartments that surround the center for miles.