I play 40K on my own quite often (because once a week is not enough for this guy) What I tend to do is set up sort of like planet strike. I'll set up a fortress and defenders and then make a list and see how things go.
I did this last night with 1500 pt kan wall with some nob bikers and big meks against about 3000 points of IG with 100 guardsmen, 2 LR 3 Mecvet squads, and a shit ton of heavy weapon teams.
You cant get a better answer than that.
I also play Solo quite a bit, not weekly, but as much as possible. I found the best way is as described, to have one force either entrenched in a impregnable position, and assault it with everything you got, or to play as though a squad or two are storming a small space ship or large underground complex. Either way, the key for me has been to have one army's freedom of mobility tied down, either by a fortress or by limiting movement to corridors or groups of rooms.
The best inspiration I had for this kind of play was "Storm of Iron" an Iron Warriors novel about the siege of an IG planetary fortress. Setup correctly, these kinds of battles last forever, and can be really fun, since the home team really doesn't need much in the way of tactics, other than duck and cover, and annihilate anything that comes in range. A great book, re-invigorated my interest in playing with.... Er, by
The easiest, fastest, cheapest is to play out a space hulk mission, so you can use just a flat map as the game board (The tiles from Warhammer Quest work well. As someone else referenced). To be real honest, the first few times I did it, I used the board from Clue. A few models and the clue board, and you are in business for an hour.