Assuming you can access the Nice railway station and you are reasonably ambulatory, there's no need to rent a car to get to/from Monaco. TER services to/from Monaco are quite frequent (roughly every 20 minutes or so), cheap at just over €4 for a one-way ticket, and Monaco is generally walkable, though be aware that there can be elevation/terrain changes.
That being said, I find Monaco to be generally overrated and not worth an overnight stay, but your opinion may differ (particularly if you have lots of money!)