I'm a broken record on this one, but I believe Chez Pascal on Hope St makes by far the best food in Providence, albeit at a fairly high end. Nothing too scary for someone from LA though, price-wise. Their food is prepared with immense care using the best-quality seasonal ingredients. I really feel confident that nobody is operating at as high a level. For an out of towner who really wants to be wowed, it's the place. The desserts are the only flaw in my mind--I find them hit or miss. Fairly convenient to Brown, though not walking distance.
OK, I'll get this started but I should warn you that it's been more than a year -- and in some cases longer -- since I've been to many of these. I'll be curious what RI chowhounds who eat out in this area more frequently than I do have to say. I'm going to stick with mid-priced choices because our high-end restaurants have been discussed pretty exhaustively on other threads. I would say, though, that if you're dying to try al forno, you might want to consider eating out in their very pretty courtyard if it's a nice Sept evening. Their pizzas, salads and homemade desserts really are great -- and if you're splitting them, you won't have to get a second mortgage.
I've found Paragon on Thayer St to be consistently good, though you won't find it particularly innovative or reflective of the region.
A few blocks away, I've always liked Sawadee's (on Hope St) for Thai food.
In the Wayland Sq area, there's Red Stripe. I much prefer their lunches to their dinners. I love their BLT with smoked salmon (which they make themselves). And if it's a nice day, they throw open their large front windows, which makes it particularly pleasant.
Around the corner from Red Stripe is Haruki's, a Japanese restaurant with good sushi. They have a fried soft shell crab, which is usually -- not always -- quite delicious.
Over on Hope Street (toward Pawtucket), I like Chez Pascal, though it's been almost two years since I've been there. Good traditional French food.
Also on Hope, I've heard good things about Blaze, but still haven't gotten there.
I used to like Pizzico on Hope St. quite a bit but my last dinner there left me cold -- and service was really slow.
There's a barbecue joint at the end of Hope (in a shopping center at the Pawt/Prov line) that I haven't been to yet, but it's on my list.
I like India -- which everyone prefaces by saying "It isn't authentic, but..." And they have a nice patio for outdoor dining. I love their little lamb chops. And the bread is always good. Someone who has been there more recently than I have said the menu is changing and they're trying to do other cuisines as well as Indian, which is probably a mistake.
There's a new Asian (I think maybe Vietnamese) restaurant on a side street off Thayer. I'll be interested to hear from chowhounds on that.
I've always wished we had some kind of shore dinner hall for lobster, steamers, etc. that I could send tourists to in Providence, but we really don't. Hemenways specializes in seafood, but I haven't been there in years so I'm hesitant to recommend it.
Hope this helps.