A good grill smoker combo? Does it exist?

Lots of good suggestions here.
Everything from breakfast to supper can be cooked on a Weber kettle, get the 22" if you go that way. Using the fuse, or snake method its about as close to set and forget as anything else.
As has been said, a WSM will purr right along all by itself for several hours.
The Green Mountain Grills work very well and within your budget, I have 2 of those. Take out the diffuser system and slap a set of grill grates on it and it will sear very well.

Memphis Wood Fired Grill is the best and double wall SS and works just great....

They are pricey, but you can leave to your kids in your will...LOL...

You get what you pay for in this instance, I got one and don't regret it one bit.