In addition to
Glenn's, there are
Fahlstrom's (as in Glenn Fahlstrom) and
Fish Bar. Both have excellent seafood, but neither is overtly upscale, and it sounds like you're looking for a bit upscale. If so,
GT Fish & Oyster and
Shaw's Crab House are both still terrific. GT Fish is one of my favorite restaurants in the city, and Shaw's is the most evocative of New England seafood restaurants. All have discussion topics here on LTH (
here,
here, and
here, and
here).
Other upscale candidates include Portsmith (liked it), Hugo's Frog Bar (liked it), Catch 35 (went some years back and was disappointed), and some places I haven't been (Eddie V's, Truluck's, Ocean Cut).
Some of these are downtown in River North and the Gold Coast, which may or may not be included when you think of the North Side. Check all of their online menus to see which also offer sufficient vegetarian choices for your needs.
Oh, and Eater has a listing/map of
20 of Chicago's Best Seafood Restaurants.
My Top Picks: GT Fish or Shaw's.EDIT: After checking out their website menus, the vegetarian choices at GT Fish are extremely limited (an eggplant side, and french fries), so that could be a problem. (It's not a great place for carnevors, either, as they only have one meat dish.) Shaw's has numerous salads and sides, like most places.