I used to live near there, and my father worked near the river in Old Town. I used to walk around old town for the scenery. It is beautiful!
My favorite place is The Torpedo Factory, on Orinoco St (I think), on the waterfront. Artists rent spaces to work and sell their art.
Bilbo Baggins is a good restaurant for lunch, but busy. It's a bit on the $$$, but worth it. Queen street, I think.
The George Washington Masonic memorial on King Street. You can't miss it, it looks like the lighthouse of Alexandria. The view is worth the ticket price, but the exhibit is kinda dry.
You can also rent a bike in town at Bike and Roll on Wales Alley, and go down a beautiful pathway to Mount Vernon. SO Worth it! You can also go north to Arlington and Georgetown, but it's a trek.
Explore and discover. Have fun.