In general, most alpine plants won't grow well indoors simply because you can't duplicate their alpine environment inside - cool temps, lots of sun, and winter. But there are some that can take a lot of abuse, environmentally speaking. First, don't try plants native to high, cold mountain peaks. Lower elevations will be more humid, comparatively, and a warmer climate. Plants there, hopefully, will be more adaptable. Many sedums, especially the small leaf types might do well, and I have overwintered Delosperma cooperi inside without any problems. I would think any Delosperma species or related genera woould do fine. There are so many, and some native to almost the coastline in South Africa. Crassula species might be another option, and the many cactus genera.

Now maybe someone with some experience will give some advice. LOL