Theres a nice mosque on the corner of Lachem st.
No seriously, what are your hobbies and interests?
Was gonna say, Bodrum Isn't the most exciting place to visit but if your relaxing that's all good.
Turkish baths are a must in Bodrum, full day of steaming baths and the additional massages and scrubs.
If you like your nature and scenery take a trip around the peninsula, best by minibus as you get to see almost every cranny and is cheaper then a 2 course meal.
You could also take a boat trip around the island, food is usually provided and there will be a stop off where you can swim in the sea or sunbathe etc.
That's about it really lol.