Portsmouth has a lively bar scene concentrated in the streets around Market Square. Craft beer is well represented — the Portsmouth Brewery on Market Street was one of the first craft breweries in New England and still makes consistent, unpretentious beers. Earth Eagle Brewings on High Street specialises in unusual, sometimes hop-free beers using herbs and botanicals; the results are worth trying even if you're not a beer enthusiast.
For coffee, Breaking New Grounds on Market Square has been the gathering point since 1992 — good espresso, tables outside in summer, and a reliable wifi connection that makes it popular with remote workers and students. The atmosphere is what a town café should be: lived-in, slightly noisy, and unpretentious.
The bar scene around Congress Street and Bow Street has enough variety to suit most preferences, from dive bars to cocktail lounges, with most of them open late enough to make a proper night of it.