In reply to James Malloch:
If u go on to the climbing in gothenburg Facebook group (search för Klättring Göteborg med omnejd) they all speak English and you may be able to sort out a hire or lend situation.
For bouldering the one place to go they say is the island of Hönö (https://gbo.crimp.se/hono/) - access easily enough with public transport and am sure u can sort a rental bike also easy. For sport, there are some sport walls in Utby (can get the bus there from town - the number 58 should see u right). Check the Utby page on ukclimbing- I think Rabies wall is the only full sport crag. There are other sport only crags also in the area but tbh it is most famous for its granite trad climbing.
If it's raining then there are 3 top quality indoor climbing halls too inside the Town, all with different character - klätterfabriken (old school hard) klätterdomen (offers all forms and plenty of bouldering and auto belay) and klätterlabbet (more mainstream, less bouldering but big walls)
If u need more advice PM me and depending on how long you need it I can lend you a guidebook. Also worth swinging by the local climbing shop Fjällsport and get tips from the guys there too. U may even be able to arrange a rental of a mat through them if u give them a call- they all speak English excellently.