GPS with linux?
On a little PC?

YES!

I have an EEE701 4G and an inexpensive USB GPS dongle (BU353). I installed kubuntu9.10 and TangoGS and JOSM (Java OpenStreetMap Editor) on my EEE and it all works together brilliantly. No touchscreen though.

Having installed all the software I needed I almost ran out of space on my 4GB SSD, so I plugged a 16GB SD card in the little slot. Partitioned the card as 5GB for / and 11GB for /home. Plenty of room for maps and route-traces now :)

Setting all that up with grub2 was a PITA (but an interesting project). All in all, it has taken me three weeks to set it all up, but it was a very part-time project for when I was bored and just to see if linux was up to the job.

It certainly is!

Route-planning software is not so good. I can read a map though, if I know where I am.

I am very happy with linux and GPS. Everything works very well.

I gave GPS dongles to two (teenage) people for Xmas (they have EEEs) and I await the outcome of my HOWTOs. One is certainly working (but required parental support to follow my HOWTO).

You made the right choice - get an EEE.