I was born and grew up in Bangkok, Thailand, but I went to high school right here in Medford, so I've had a few years to get to know the area. Tufts sits on the line between Medford and Somerville, and here are the places I'd point you to if you're looking to get off campus.
Medford Square
Medford Square is a short trip from campus and has a lot of good food packed into a small area.
Tenoch Mexican is my first pick. It's a small spot on Riverside Avenue, nothing fancy, but the tacos and burritos are affordable and really good. The asada con queso and chorizo are what I usually get. Tenoch isn't only in Medford Square either, they have a few other locations around the area, and they're all good.
Tom Yum Koong is a Thai place on Forest Street. I really like the variety of their Thai street food options. A few I'd recommend: Khao Moo Sam Chan Tod, which is crispy fried pork belly over rice, Khao Kor Moo Yang, grilled pork neck served with rice, and Khao Moo Dang, sweet red barbecue pork over rice.
Nijiya Sushi is all-you-can-eat sushi. You order off a list as you go and everything comes out fresh, with a two-hour limit that's more than enough time. Go hungry and go with friends, but pace yourself so you don't over-order and end up stuffed trying to finish it all.
Colleen's is part ice cream shop, part diner. The ice cream is the main draw, but the sandwiches are good too.
Wright's Tower
Wright's Tower is a stone tower up in the Middlesex Fells. It's a short hike, about fifteen to twenty minutes, with a steeper part at the end. You get a clear view of the Boston skyline from the top. Parking along the Middlesex Fells is free. The tower itself is usually locked, but the view from the rocks around it is the best point.
Mystic River Reservation
If you want something flat and easy, the Mystic River Reservation has paved paths right along the water that are good for a walk, run, or bike ride. The sunsets over the river are nice and there are plenty of benches to sit. Expect to run into some geese.
Assembly Row
Assembly Row is over in Somerville, right off the Orange Line, and it's the spot for shopping, food, and activities all in one place. There's an AMC theater with IMAX, bowling, outlet stores, and a Trader Joe's. For food, the Smoke Shop is my go-to for BBQ, and Ernesto's is good for a couple of pizza slices. The garage is free for the first few hours, and there's a big parking lot too.
Davis Square
Davis Square is a quick trip from campus and right on the Red Line, so it's an easy launch point into Boston or Cambridge. The Somerville Theatre is the landmark here, an old theater that shows movies and hosts live shows. It's worth going to at least once. For food, Eat Greek is great for gyros, Dakzen is my pick for Thai street noodles, and Mortadella Head is the place for pizza.
That's my list. None of these are far from campus, and they'll give you a good feel for the area outside of the Tufts bubble.