Costco charges about $3.99 in my neck of the woods for a 12x18 IIRC; for that it’s worth experimenting. get a print made of the full pic, get a print made of the center cropped to half size (say the tower) so that if you printed the whole thing at that enlargement it would be 18x30 or something. That should give you an idea. Experiment trumps theory.
Many photo printers work their own magic on the image so you get a smoth picture, not a pixilated bunch of squares like the monitor may show in blown-up view. They want to help you and get repeat business. I have a Fuji 4900Z image, 2.4MP interpolated by the Fuji to 4MP and printed 11x14 and it’s a bit grainy but very nice and pretty sharp. I suspect most limitations nowadays are the lens quality of the smaller P&S camera, not the sensor or JPG artifacts.
As others point out - it depends on how far away you are looking at the picture from. For magazines, from 12 to 18 inches away, 300 to 400dpi (dots or pixels, details, details…) is good. For regular photos on a wall, 100dpi to 150dpi full colour is good. For posters to admire from 3 feet away, 50DPI might work. YMMV.
Blow it up in your monitor so the picture is 3 monitor-screens wide; that’s about 3 feet by 2 feet or so; and since your monitor is probably 1 foor horizontal and 1280 pixels, that’s about 100dpi.
Every time you re-save a JPG you lose a little bit of information. This is not a big deal if you edit your original JPG, crop it, and then save as a second JPG. It is if you are going to edit, make a few changes, save. Come back each day for a few weeks and open the work in progress, tweak it some more, then save as JPG again. Even worse if you crop or something to change the boundaries of the 8x8pixel tiles that JPG works with. If you must do this, store everything between the original and the final product as lossless like photoshop PSD or TIFF.
NEVER NEVER OVERWRITE THE ORIGINAL CAMERA IMAGE. Treat this as we used to treat the negative in film. It is your best starting point for every new attempt to crop, edit, enhance etc.
If you really want to enhance resolution - you can’t do those stupid tricks like CSI and the movies do, where they blow up a pixel into a recognizable face; you can, however, use programs like (IIIRC) Fractal Magic to enhance the sharpness of an existing picture so you can resize it as say, 10MP or 12MP.