Echoing a few other comments:

Starting from the Inner Harbor area, Maryland Ave has a dedicated bike lane that runs through the city. Lots of stop lights but it is relatively hilly so it's a good warm up for once you get out of downtown. Swing on to Falls road right next to Baltimore Bike Works then ride up through Hampden following the signs for Roland Park (this route also brings you past Lake Ave and adjacent roads which have some absolute beasts of hills so when you get to Lake Ave definitely poke around). Loop Roland Park for some good hills and lake views then get back on Falls Road and head towards Joe's Bike Shop in Mt. Washington (to add as much distance as you want head the opposite direction up Falls Road then double back). Cross the bridge across from Joe's and link onto Jones Falls Trail. Follow the trail until you hit Druid Hill and take a left upon entering. This brings you to the big hills others have mentioned, ride up and down to hearts content. When tired, exit Druid Hill by the swimming pool, take the pedestrian path back down to Falls Road, back down Maryland Ave, and you're in the Inner Harbor. If you just do the loop without and extras it comes out to ~20 miles. It's the best mix I've found of bike paths, dedicated bike lanes, and safer roads. There is also good elevation along this route, and you can double back on any hills you like or ride it in reverse to hit hills from the other direction.

If you get tired of battling cars and want to opt for a safer, flatter option, the BWI loop connects pretty directly to the Baltimore - Annapolis bike path so that is an easy way to crank out some miles without worrying as much about stoplights. Not a ton of good elevation, but not totally flat either.

Also, as long as you are hyper-aware and seek out bike lanes downtown I've found Baltimore to be an unexpectedly rideable city :)