lets see I don't go into the city as much anymore. Though technically I still live in the city lol (but I mean downtown more then anything else).
There is parking in the city but you have to know where to find it. Though honestly you can go to any city commuter parking lot and park for the day it will cost you between 5-6 bucks and you don't have to go on commuter line to find them. You can find them along the orange line and other lines check out mbta.com . You can also park with validation and alot of places in town and on market days there is a lot in haymarket that if you buy something from the market you can get validation that gets you 3 hours of parking for $1. In the north end there is a small lot that offers free parking. Point is there is parking but it will take work to find it. I personally do park in town and drive from about 10 mins outside the city to do so. Granted I could take the T but it would actually cost me more to take the T and pay for parking then just to drive in.
Also if your staying overnight. You two are young check out
www.bostonhostel.org located very close to Newbury street in the back bay much cheaper then a hotel. Also most collages actually rent out empty dorms for the night for travelers and some will include meals in cafeteria. You'll save a lot of money and introduce her to new people and potentially get a free college tour out of it. With all the universities and colleges you should be able to find accommodations easily.
Also if you have student id's bring them most museums, movie theaters, etc have student discounts. Also check out Groupon.com and buywithme.com lots of great deals on restaurants and spa stuff that you can do.
Places to go in the city: Boston public garden not to be confused with the Boston common lol ok their both pretty but only one has tons of flowers and the swan boats. Definitely take a ride on swan boats there fairly inexpensive and very historical, also fun to watch another teen peddle you around =).
If you love to walk try the freedom trail. Buy the guide book or get a free pull of sheet that lists all the stops at the visitor information center in the Boston common. Don't feel obligated to walk the whole thing unless you really want to or to pay to enter all the sites there are lots of sites that are free.
Search online beforehand for discounts on tix for trolley tours and the like. Bostonusa.com has tons of things to do. Check the city of Bostons web site for a summer in the city guide as well as arts Boston guide. Both should be out if your vising after graduation. Lots of free fun stuff to do like, concerts, festivals and annual events. As well check out museums for exhibits and venues for concerts you may want to attend.
If you have time and your coming for multiple days plan a short trip outside the city. I think someone else mentioned Salem and Plymouth. Honestly I'm all for visiting certain places during specific times of the year so if its late summer early fall go to Plymouth or Salem if its summer hit the cape or Rockport. All are day trip within about an hour or less of the city other then cape cod plan a few hours of driving for the cape or you can take a harbor cruise to the cape from the Boston Harbor. You could also take in a whale watch or tour the harbor islands.
If you love seafood eat at the Union Oyster house. Its the oldest continuously run restaurant in the country and I'd probably spend a few hours in Harvard square a few hours if you plan to visit Harvard University's Natural History Museums. Maybe take in a baseball game at Fenway Park.
feel free to pm me with any questions I was born and raised in the city.
Boston's a little city with alot to do. I hope you have a great trip.