My friends who live in Baltimore and have a toddler like Patterson Park, so maybe Patterson Perk coffee, which looks to be near the playground on the south side? 2501 Eastern Avenue.
For what it's worth we have been to their favorite neighborhood hangout, Ale Mary's, which looks like a bar but is very kid friendly with a full menu (kid's menu, tater tots!) and opens at 10 am on Saturdays...