I would try Pudding Stones on 3rd Ave @ 82nd, East side of Ave. Nice wine selections, not sure how large thought. Right around there is The Gael Pub and Wicker Park. It's a little closer than the places on 2nd Ave if you're walking in nice clothes. You didn't mention what time of day, the Gael and Pudding Stones may not open until late afternoon but Wicker Park serves brunch so am sure it'll be open.
1457 3rd Ave, New York, NY 10028
1469 3rd Ave, New York, NY 10028
2nd ave is probably your best bet. How far are you willing to walk? I really like Heidelberg which is a german bar/restaurant between 86th and 85th on 2nd, but it's smaller and might be too hokey (think Germany at the Epcot center at Disney world) for your tastes. If you walk further there's Doc Watsons and Johnny Foxes' around 79th and 78th. and 2nd ave- both typical Irish bars that serve food. If you're looking for something nicer there's Niche around 85th and 2nd and I think Uva, which is an Italian restaurant closer to 78th, has a bar too, but it's not huge.
1486 2nd Ave, New York, NY 10021
1490 2nd Ave, New York, NY 10075