Probably too late but there are probably twenty places you can go.
**Sharkey's is right on Eastern Avenue and it's definitely a burger/beer type of place.
**I'd second Annabel Lee's and also suggest Birches as both have really good food.
**Some other places: Geckos (SW); Yellow Dog (more upscale); Saute (bit further from the park); Kislings and Tyson's Tavern (closer to Fells Point); Bleachers (sports bar); NicDevin's and Lagers are a bit further away from the park too (both are typical Baltimore bar).
I agree, Annabel Lee is good and you're fine to sit alone. They have resurrection ale from Brewer's Art, so that's always good!
If you go to Butcher's Hill by the park, Life of Reilly is a good Irish Pub, they have burgers. On E. Fairmount Ave
If you go Canton side of the park, check out Yellow Dog Tavern on the corner of Potomac and Foster.
Another good parkside restaurant is Three, on the corner of Linwood and Baltimore St.
Good atmosphere, appetizers, have sandwiches and entrees.