What do you do after a Level 1 playthrough?

Just wondering what people normally do with their character after finishing (assuming you aren't trying to go to NG+ 7 with it).  Do you drop a couple of points in so you can use a bit more variety of weapons?  Stay at low level for coop?  Invasions?

I'd push it up to SL11 and do co-op in the Burg. You can't really do low-level invasions unless you're okay with menu-swapping between powerful weapons/armor and unupgraded weapons/armor constantly. I've tried and it's just exhausting. During low-level invading, you can invade new players, new players using the megamule, really high-level players, and everything in between. Often it's hard to distinguish between them and/or figure out what you should use against them to have a fight where neither of you gets OHKO on a single R1 swing. It's just not worth the time and effort. But that's just my opinion.
I've got a Siegmeyer cosplay build that I use for low-level co-oping and for invading ~SL50s in Sen's and AL. http://mmdks.com/3izd

Cool...I don't really like invading people's games.  I like PvP in the forest at high levels, but it's more like an arena, now.  Some ganking, but some good fights as well.  I was thinking I'd just add a few levels, like you said, for the good weapons, and then coop.

Some people just leave the character for SL1 coop with those who need help, if you wanna invade there's that too.

Either push all the way to NG+7, or summon / get summoned in the undead parish.

I've kept my SL1 as an SL1 just because. I sometimes get on it to help other SL1 runners with problem bosses like Kings and OandS. I mean I bothered going to Ng+++ and collecting these rings so I can potentially have 32 casts of GC available. (Though I find one is often enough and use my other spell slots for other spells. GFB and regular Combustion usually. Swap one of the seance rings off after applying PW for Bellowing)

Yeah, consider keeping your guy at SL1 just because you'll sometimes get the urge to advance him through ng+ when you're looking for a different challenge.

I've got two SL1 guys on ng+. One of them did the "unique weapon per boss challenge" that DSG78gaming came up with.