If you're looking for an unfussy place to grab a burger or salad, and a pint of beer or glass of wine, Cato's is great. Hannah plays trivia here (most) Monday nights.
Literally a half-block from our house, the Morcom Rose Garden is beautiful.
Lake Merritt is where we had our first date, and where we got engaged! You can go for a walk around the lake, sit on a bench and drink a coffee from a nearby coffee shop on Lakeshore or Grand Ave, or visit the Bird Sanctuary.
If you're staying at the Sheraton, we highly recommend grabbing a meal at Public Market - there are a number of vendors offering everything from deli sandwiches to ramen and Peruvian fare.
The Oakland Museum is near Lake Merritt and has a range of exhibits focused on the art, culture, history, and natural history of California. Check out the open air Koi pond on the second level. Friday Nights, one street next to the museum is closed down for food trucks and there is live music, and a bar in the museum.
One of our favorite spots for used and new books.
Running 8.4 miles from the Bay Bridge to Berkeley, the Eastshore state park has a beautiful bayside trail to take a walk. There's a portion of the trail not far from the Sheraton Four Points. Park on the Frontage Road just north of Powell street, and walk as far down as you'd like. If you're feeling more adventurous, you can walk the pedestrian path on the eastern span of the Bay Bridge all the way from Emeryville to Treasure Island. Info here: http://baybridgeinfo.org/path. It's about 7 miles, but a unique and beautiful urban trek.