You can't use the dining plan to eat at a bar. If you use the dining plan it is best to make ADRs at a regular restaurant. And you can only get it if you have a Disney room/tickets package reservation, have an annual pass, or are a DVC member.
Anyone of any age can sit at a bar - you just can't order alcohol if you're underage.
This is my bar list:
California Grill lounge – full menu available
Tune In Lounge (adjacent to Prime Time Café) – full menu available
Jiko – full menu at bar
Raglan Road – full menu at bar
Gurgling Suitcase – full Olivia’s menu available at bar
Rainforest Café – full menu at bar
Yak & Yeti – full menu at bar
Citricos – Full menu is available at counter/bar seating inside restaurant. I believe, but am not sure, that you can order Citricos dishes from Mizners lounge.
Rose & Crown – pub menu (cheese and fish & chips available at the bar)
Flying Fish – full menu at counter seating
Turf Club – appetizer menu at bar
Tambu Lounge – appetizer menu at bar (selections from Kona)
Territory Lounge – appetizer menu at bar
Martha’s Vineyard Lounge – appetizer menu at bar
Rix Lounge – appetizer menu at bar
Bluezoo – bar/café menu (limited selections, no desserts)
Crockett’s Tavern – food available
River Roost – appetizer menu at bar
Crew’s Cup Lounge – appetizer menu at bar
The Wave – appetizer menu at bar