I definitely agree with some of the earlier comments that driving in the NE can be sketchy in March. I'm not sure what part of Australia you're from, but if you're not used to driving in snow and ice, it can take some getting used to. You've definitely got the right idea with renting a car instead of trying to take buses or trains because they're both expensive and terribly inconvenient in my opinion. As for your locations, I've been to Washington DC several times and I love it. If you have any interest in museums the mall is loaded with tons of museums and admission to all of them is free. There's also an ice skating rink on the mall that is kind of tiny (and show up early for tickets, they run out fast) but I think it's nice just for the atmosphere. My favorite museums there are the Museum of Natural History and the National Gallery. There's also the Vietnam memorial, the Washington monument, and lots of other nice monuments in the area. There's also a lot of shows. If you like band music, the President's Own the most prestigious marine band plays concerts in DC (not sure if they do it during winter though) and the concerts are free of charge.
I've only been to Baltimore once. I haven't been to the aquarium there, but it seems to be a pretty popular. When I was there I went on a dinner cruise that left from inner harbor. Nothing to exciting but it was a nice evening.
Philadelpha is a nice place to visit. There's a lot of historical places there to see: the liberty bell, independence hall (it's free to visit but you'll need to get a ticket as they only take so many people in at a time). There's also a street called South Street that tends to be popular for young adult night life.
New York, I think is well known enough that I can leave that one alone. 😊
I absolutely love Boston. There's a lot of shopping. There a path called the Freedom Trail that is actually marked on the city's sidewalks. It's pretty long and requires a bit of walking but it takes you past a lot of historical buildings. Harvard is a hop skip and a jump from Boston by metro. Another place that is nice to visit in that area that is easily reached by train is Salem. It's the location of the witch hunts and it's not a big place at all but I really enjoyed visiting there.
I haven't been to Montreal or Toronto but I went to Niagra Falls with my family. It's a really nice place to see and I think that the Canadian side of the falls is much nicer than the American side (in terms of view of the falls and just general niceness). There's also a butterfly conservatory on the Canadian side that we didn't get to go to but it sounded really nice.
Of all of your destinations, I'd say you could easily leave out Detroit and Cleveland and not miss much. I've heard from friends that live in Michigan that Detroit is not a nice city. I honestly think that you'd be better off driving back through Pennsylvania from the falls. I've driven from my home to the falls and I've also driven through Ohio and into Michigan a few times and it's a whole lot of driving. In my opinion, Detroit is not worth it.
Pittsburgh I think you could take or leave. I went to university an hour away from Pittsburgh and I've only been there a handful of times. It's really just not that exciting. It's also really, really confusing to drive there if you're not familiar with it. I've never gone there and didn't get lost, even when I've gone to Pittsburgh with friends who live there. There's some nice parts, for example, the water front is nice and people really like going there.
One place that I'd like to introduce you to in Pennsylvania is Lancaster. It seems that you are going more for cities, but just in case you also like wilderness, Lancaster is a large farming area and lots of Amish people live there. I know some people from Western PA who like to go to Lancaster to relax. There's lots of beds and breakfasts there and it's supposed to be really nice. I've never gone there to spend the night as I live quite close to there myself (and there are plenty of Mennonites up where I live). A friend of mine came to visit me from Germany and was really interested in the Amish. Some how he managed to meet a family up north of Pittsburgh, not sure exactly how he did that, contacted someone online...
Anyway, I hope that this is helpful, if you have any questions that I might be able to help you with just send me a message. 😊