You should support Västerås in the second division, HockeyAllsvenskan
It depends what kind of supporter you are, do you want your team to be a league contender, an underdog or do you just go after their brand?
As you already support a capital team, why not Djurgården? Classic club, most titles, best hockey fans in Sweden, good attendance etc. Con: They recently got promoted back to the SHL, so they don't have the strongest team, although they are a playoff team.
Malmö Redhawks has the best logo in my opinion, plays in the best arena, pretty good jerseys. Con: Newcomers this season, they don't have the best team and I'm doubtful that they will reach the playoffs.
Växjö is just awful, throw them in the trash bin
Örebro, don't even consider them
Rögle is pure garbage
Karlskrona is an option if you want to feel bad for a team that barely wins and will most likely get relegated in spring
Skellefteå has a good team, they're a fun team to watch on the ice. Con: Can't really come up with one, unless you're not a fan of their brand
You should definitely support Luleå if you like Minecraft
MODO is one of the most famous clubs outside Sweden as they've produced some of the best players (Forsberg, Sedins, Näslund, Hedman etc.). Their jerseys are pretty good but their team is really bad this season.
Linköping have a pretty good team every year, but they always manage to choke in the playoffs. I've never been a fan of their brand but that's just my opinion
HV71 has been a good team, but they have some problems in the club. They barely had a coach before they hit the ice this summer!
You didn't like Frölunda, so I guess they're off
Färjestad, meh..
Brynäs is a classic club as well. They've never been relegated from the SHL/Elitserien and became Swedish champions not so long ago. They got a pretty good team this year and clearly have the best jerseys in the league (no ads on the jerseys). Their logo is decent though..