I was in Michael's craftstore a few days back, and picked up a 12x18 sheet of "Creatology Foam Sheet" - it's designed for kiddie crafts, 2mm or so thick, and available in a wide variety of (mostly awful) colours. I snagged a white sheet to experiment on, figuring if it didn't take paint or otherwise work out, I was out nothing but $1.50 for the sheet and a bit of time.
It will hold paint - both cheap craftpaint and Reaper acrylic paint took nicely and seems to hold - it might be possible to rub the paint off, but that still takes more friction than moving figures around is ever going to generate!
It also takes embossing - I cut 1"x12" strips and 'scored' lines in it for curbs and expansion gaps, and it should make very servicable sidewalks for pulp skirmishing, at a fraction the cost of styrene while being more durable than card.
Basecoated, it hasn't warped, so that removes my last worry about painting this stuff! I've cut and basecoated 24" of sidewalk already, and I'll create more during the week until I have enough to do a bunch of roads on a Rattrap-sized 2'x2' table.
Being flexible, it's not perfect for scenic bases on more involved scenery bits, but alleyways and maybe even grassy bits should work on it - I'll have to see how the stuff takes white glue. That same flexibility means no frayed corners on the sidewalk pieces, though.
Here's the stuff in Michael's online catalog - you can't buy it online from them, however.
Pictures in a day or two, and I'll try and get some WiP shots as well.