Asking for $60-65k is not unreasonable at all and will not come as a surprise to whoever is hiring you, but be prepared for them to come back with something around $55k (could be slightly lower/higher) and not budge on that number. You don't have a lot of bargaining power here.

It's good to understand two things here - 1. these positions turn over constantly, so they are always hiring for these positions, and a zillion people apply, and 2. the people applying for these positions, by and large, are extremely unqualified by the university's standards.

You might think to yourself - why not pay people more and then they'd get better quality candidates who would potentially stick around? And the answer is that they are largely still operating on a mentality from like 30 years ago when people would start as assistants and stay there for decades. But as the city has gotten more expensive, they have deluded themselves into thinking they can continue to pay below market rate and keep people around for long (this is, of course, true in tons of other sectors).

If you're young and new to the workforce, it's a solid foot in the door. Take the offer, scrape by for a year or so, get some experience, make some contacts, and have an exit plan at the 1.5 year mark. You should be interviewing for a new job no later than 2 years after you start, maybe sooner. Bounce to a different university (this is crucial), get a 20% pay bump, and repeat that in another two years. University gigs, on the whole, are fairly low stress and flexible (lots of work from home opportunities), with decent benefits. Some are worse than others, sure, but there's job stability and the pressure isn't as bad as working in a for-profit place. Some places will give you the chance to earn a free degree. You will never make as much money as the for-profit sector but if you're talented, you can definitely move up the ranks to a well paying job even by Boston standards.

Good luck on finding a studio you can afford on $55k a year, though. I'd get used to the idea of living with roommates for awhile.