It's clear that, if it's within the budget, the Inner Harbor is where you'd want to stay. I don't think anyone is disputing that.

If downtown is too expensive and you're looking for alternatives, I'm not sure BWI is as dire as it's been made out to be. First, the MTA site shows last light rail service departing Camden Yards at 12:02 am, arriving BWI 12:36. Not sure why shinbal has shorter hours, so I guess it's worth checking with MTA to confirm.

Second, if you're arrving BWI, you're going to have to deal with airport-area transport at least twice, anyway. You're out all day Friday, and Saturday should be a full day if you do Preakness right. It's going to be a pain to get to/from Preakness under any of the mass transit options - but again, it's an all-day affair, and you'll be in it with a lot of other Preakness-goers. Depending on where you stay, though, Thursday could be a problem around BWI - it's true that the area where most of the hotels are clustered really offers nothing.

So, assuming Inner Harbor is out and you want to avoid renting a car, there may be other options (north - Hunt Valley?), but no one has offered anything yet. Otherwise, you'll have to decide how much of a premium Inner Harbor is worth. You've got a variety of opinions on how practical BWI really is, but it can be done if you want to.