Your first challenge might be to find an actual pub. While communal drinking absolutely was an important part of Early Medieval social life, outside of select urban sites, you're unlikely to find a dedicated building specifically to pop into for a drink.

Your options depend somewhat on your occupation and status: if you were a member of a religious community, whatever your office, you might go to your House's refectory, where your main beverage of choice would be ale. As the character of the Initiate in Ælfric's Colloquy explains:

I drink ale, usually, if I drink at all, and water if I have no ale... I am not rich enough to be able to buy wine.

The main reason ale is plentiful but wine is not is that anybody with some left-over grain can brew beer, while wine has to be imported. Those with available grain would brew their own ale, and, if they had enough, sell some to their neighbours or invite them around for a drink. In the case of the Initiate in the Colloquy, the House would most likely have had its own brewing facilities. Lacock Abbey in Wiltshire is a fine example of a (former) religious community which still has its brewing house intact. That particular example dates from the early 13th Century, but the overall principle and design is unlikely to have changed considerably in the intervening period.

Depending on the surplus available to the community, its own consumption and the mercantile spirit of its seniors, it's entirely possible that such a community would have sold ale to the local villagers. Otherwise, brewing would have been carried out small-scale. Your best bet at a 'pub' might in fact simply involve having a friend with a surplus of grain and a wife with some time on her hands to make the beer. This may simply be in the context of having friends over to share a meal. Again from Ælfric's Colloquy:

let us meet together at the ploughman’s house where we may have food for ourselves and fodder for our horses

Our sources for urban life in this period are somewhat scarce, but later evidence does point to commercial brewing in urban centres. Notable 14th Century writer, pilgrim and holy woman Margery Kempe reports running a small brewery in Lynn (and apparently being quite good at it), while the 15th Century poem London Lickpenny depicts a number of taverners selling ale alongside stews, pies, and a wide array of street food such as hot peapods, mackerel and herrings, hot sheep's feet and rissoles.