Helping out the people in Freeside or helping out the Boomers might be a good choice. The Boomers are an isolated society so you wouldn't be drawing attention to yourself elsewhere. The only really tricky part that people complain about is getting blown to smithereens by the artillery, but I've always hugged the left cliff face and sprinted down that way in one go, and I've never died doing it.
You do get quite a bit of attention doing the Freeside quests, but it just means other people in Freeside know about you and sometimes give nice comments or give you gifts. You also stop getting attacked by random thugs eventually. If you want to spare all of the companions, don't hand Cass over to the Van Graffs.
Once you've gotten acquainted with the Boomers, take Veronica with you and go to Hidden Valley. The Brotherhood have a few long, drawn out quests but apart from the Vaults quest they consist of "go there, pick that up" or "travel here, talk to this guy". They offer decent XP.
If you have Veronica with you, you can outfit her in the Brotherhood T-51b you'll no doubt pick up. It's also one of the only two roads to acquiring Power Armour Training so the sooner you do it the sooner you get to use PA, if you so choose.
There are some fairly simple quests at the Mojave Outpost on the bottom left of the map.
The Crimson Caravan Company have some fairly simple quests as well.