Cockeysville/Timonium is very suburban so yea you'll just be experiencing more suburban life. There are other suburbs that have "city-like" features; Catonsville and Ellicott City come to mind and the commute from there to UMMC will be easier than from up north since you get to avoid 83 and downtown traffic. There's also Mt. Washington that's within city limits but very suburban-like and has a small main street and other small strips with restaurants, bars, shops, and a Whole Foods. Mt. Washington is also easier to access downtown since there's a light rail stop and you could use that for commuting if you wanted to as well.

Otherwise, there are some places in the city that will give you some more outdoor space but it's going to be dependent on your budget. Hampden (anything north of 37th street) has some homes that have decent sized yards. Otterbein is a nice community that's really close to downtown and has a lot of shared outdoor space. Along the same vein with shared outdoor space, anything around Patterson Park might work too. You won't have much "private" outdoor space save for maybe a small patio/offstreet parking pad and maybe a roofdeck though.

Really the appeal of living in the city is being able to walk to so many things if you want so you'd have to figure out if that is something that's really going to stress you out or not. Also I know very few people that live in the city and don't drive to go get their groceries still. If you're lucky enough to live within a few blocks radius of a grocery store it's probably not a big hassle, but otherwise everyone I know that lives in the city (Canton, Fed Hill, Patterson Park, etc.) drives to their grocery store(s) to get groceries. Or there's always the option to get them delivered.