I'm writing a strange little ukulele tune that goes G-G7-C-Cm and then repeats, basically. But I'd like it to repeat to a different last chord/last two chords but I'm having an issue finding a chord that works well but also sounds "finished". It would play out like this - G-G7-C-Cm, G-G7-new chord-new chord. If you have any suggestions please let me know, I'm having a lot of trouble!
Without seeing the melody, I'll just guess. The G-G7 really calls out for some type of C chord so a small change might be G-G7-Cm-C. G7 is nicely followed by either an Am or Ab chord perhaps G-G7-am-D7, setting you up for a nice repeat (if this doesn't clash too much with the melody. Other possibilities are G-G7-C7-F7 or G-G7-C-F7 (keeps the Eb note).
If your melody gives enough time, C64-G7-C-Cm or G-G7-Am-D7-C64-G7-C-C really sounds finished. Adding some chromatic stuff: G-G7-Am-N6-C64-G7-C-Cm. There are other possibilities.
The chords are in G, but with some borrowing going on. Very cool sound! To continue on, I'd try Cm7 and F7 for a sadder sound (Backdoor!), or one could use A half-diminished and D7 for a brighter ending. Additionally, if you want more of a turnaround feel in the middle, one could replace the G with an Em the second time around, then Edim7, Am7, D7, for example.