Low lunar orbits
For low lunar orbits it's a challenge because the Moon as a lot of mass concentrations or mascons near the surface, and these will continue to perturb a low orbit and ultimately bring it down to impact the surface after months or at best years.
There are certain sets of orbital parameters, basically certain combinations of inclination and semi-major axes... these are called frozen orbits because while perturbations affect them they tend to remain somewhere near the same orbital elements rather than veer into surface impact.
Lunar frozen orbits
Through a study of many lunar orbiting satellites, scientists have discovered that most low lunar orbits (LLO) are unstable.3 Four frozen lunar orbits have been identified at 27°, 50°, 76°, and 86° inclination. NASA expounded on this in 2006:
Lunar mascons make most low lunar orbits unstable ... As a satellite passes 50 or 60 miles overhead, the mascons pull it forward, back, left, right, or down, the exact direction and magnitude of the tugging depends on the satellite's trajectory. Absent any periodic boosts from onboard rockets to correct the orbit, most satellites released into low lunar orbits (under about 60 miles or 100 km) will eventually crash into the Moon. ... [There are] a number of 'frozen orbits' where a spacecraft can stay in a low lunar orbit indefinitely. They occur at four inclinations: 27°, 50°, 76°, and 86°"—the last one being nearly over the lunar poles. The orbit of the relatively long-lived Apollo 15 subsatellite PFS-1 had an inclination of 28°, which turned out to be close to the inclination of one of the frozen orbits—but less fortunate PFS-2 had an orbital inclination of only 11°.4
- 4Bell, Trudy E. (November 6, 2006). Phillips, Tony (ed.). "Bizarre Lunar Orbits". Science@NASA.
Another problem with low lunar orbits is that any particular spot on the surface is only visible for a few minutes every pass, and you may pass over a given site for about one day a month - the moon will slowly rotate around it's axis each month while the orbit will mostly remain fixed.
Higher lunar orbits
For earth, we get 24/7 access to a big chunk of one hemisphere by going to geostationary orbits (or at least geosynchronous). However luna-stationary orbits don't really exist because the moon rotates only once a month, and by the time you would get high enough to orbit that slowly you're interacting with the gravity of the Earth and Sun too much. Not an option for the Moon.
However there is the distant_retrograde_orbit meaning far from the Moon but moving the
wrong opposite direction - counterclockwise if looking down from above (north of) the Earth-Moon system. At least two spacecraft have used this:
Halo and other 3-body Lagrange point-associated orbits
There are a whole host of 3-body orbits associated with the Earth-Moon Lagrange points, primarily L1, L2, that will rotate together with the Moon and stay on one side of it.
The most famous right now (but not necessarily the most suitable for you) is the near-rectilinear halo orbit planned for the Lunar Gateway.