Penzance would be a very good base for your short break.
You can spend the time on Sunday wandering around bits of Penzance - the main street is a "working" market town street and not particularly picturesque but you could wander e.g. from the railway station along towards the harbour, turn right by Old Lifeboat House Bistro and bear left to go up the old Abbey Slip steps into Chapel St which has a number of interesting buildings. Right up Chapel St, then turn into Parade St (on the left), go along a 100 yds and turn left to enter the Morrab Gardens. Follow the paths down through the gardens to exit at the bottom right corner onto Morrab Rd, turn left and within another 100 yds you're on the Promenade. From here you can either extend the walk by turning right and walking to Newlyn (about a mile) or turn left along the Promenade towards the Lido, the open-air pool. Continuing in this direction brings you back to the harbour area - a full circuit.
Once you have your car you'll be able to drive another nice circular route following the B3315 out of Newlyn towards Lamorna, passing The Lamorna Pottery - or maybe stopping there for refreshments. Lamorna Cove itself is lovely and should be fairly quiet in October. Then back to the B road, turn left, and continue onwards to pass the Merry Maidens stone circle, passing through typical Cornish farming scenery of fields and roads with high hedges. Turn left at the T junction at Sparnon. (If you have time, just before Treen village, take the awkward turning left to visit pretty Penberth cove. ) Follow signs to Porthcurno with its lovely beach, bay, and a little further on the Minack open-air theatre. Once you've "done" Porthcurno you can retrace your route back to the B road once more and turn left towards Land's End, if you want to visit it, or on to Sennen Cove to eat, or maybe catch a nice sunset if the weather's good.
That's probably enough for one day. I'm sure others will give more suggestions for trips out in the far west.
Incidentally, there's a novel called "Summer in February" by Jonathan Smith which is set in the artists' colony in Lamorna just before the first world war and it is based on real life events - you might enjoy reading it. In June there was a film released with the same title - I haven't got around to seeing it yet but, from the reviews, it seems it's not as good as the book!