Sea Salt is a very good restaurant right in the park. The light rail station is right across the street from the park, the station is literally in the parking lot of a restaurant called The Tipsy Steer that I have heard good things about. I haven't personally been there but the restaurant that was there before was very good with I believe the same owners. If you truly want a local experience for lunch, Matt's Bar on 35th and Cedar for a Jucy Lucy. It would take a bus after exiting the 38th St station. The Cardinal Bar is at the 38th St station and Northbound Smokehouse is a couple short blocks west on 38th, depending on what you're looking for. Another option would be to take the bus from the airport that goes down 7th St into downtown St. Paul. Lots of good food options along that route. My personal favorite that will be open during the day is probably Cossetta's.