People often say it's expensive to go out in Sweden.
Actually Swedish bars sometimes have cheaper beers as well as expensive beers — beer can be cheaper here in Gothenburg than in Oxfordshire! Your basic stor stark (5%+ beer) can be found from 35-39 kroner in some places. Gothenburg is the home of Swedish micro-brewing, so wherever you go there'll always be a good quality selection of (far more expensive) craft beers. I heartily recommend the Tullen bar chain - cheap and tasty Swedish food and cheap beer, plus hundreds of more expensive 'classy' beers.
There's also a few cheap beer places in Vasa too. These places seem to be sort of 'basement bars' that are sunk below street level, yet let in a little light. From the outside they look a little foreboding, but I suppose it's OK when you get in there (I don't think I've been in one yet, gotta give one a go).
If you don't mind paying more but want a bit more atmosphere, I would take a look in Sejdeln ("tankard") on Andra långgatan. This is a Czech place with good lager and classic rock music on the stereo, and true to its name you can buy beer in massive tankards - up to a litre! Swedish bars can sometimes be a little too bland and overly modern, lacking character. Sejdeln has charm precisely because it's a bit rough round the edges. Weirdly, this is the bar that reminds me most of English pubs. It doesn't look like an English pub, but it definitely has its own identity.
Near to Sejdeln on Andra långgatan you've got Kelly's. The stor stark is cheap here, and they serve cheap pizza too. It's a slightly weird place: they have big framed photos of celebrities and artists everywhere (I once spent 2 hours there chatting to a friend in the shadow of a massive David Bowie photo, which was spooky!). Despite the name, there's no Irish connection!
I should mention that near to Kelly's and Sejdeln there's a strip club. This doesn't mean this is a seedy neighbourhood: everything is mixed together on Andra långgatan! The strip club is in fact next door to a 'Save the Animals' place!
On Storgatan there's a 50's rock and roll bar called Skål. This place serves cheap stor stark (Norrlands Guld) and even cheap wine at Happy Hour. It's a nice little pit stop to while away hours chatting and listening to good old rock and roll. There's also loads of events going on throughout the week: an open mic, a pub quiz, karaoke and even Pokemon Go Tuesday (whatever that is!).
If you like playing music in pubs Restaurang Västerhus on Karl Johan's gatan is a loveable dive with a very popular open mic (every Thursday) and a lively 'bohemian' music scene. There's also SS. Marieholm, a pub restaurant on a massive boat that hosts a big blues jam every Saturday. If you fancy folk music there's Haket in Masthugget, which has an open Irish session every other Wednesday hosted by TIMSIG ("Traditional Irish Music Sessions in Gothenburg").
Well, that's enough for now. There might be a follow-up to this after I explore more of Gothenburg!