What type of telescope can show cliffs on the moon surface from a city location?
The main things to look for are:


Decent optics (nearly anything except those with plastic lenses).
A steady mount that points where you want to, and moves smoothly. An altitude-azimuth mount is fine because with practice you can guide at high powers.
The eyepieces should be 1 1/4 inch size or more expensive 2 inch. The older 0.96 inch are very hard to find. This lets you upgrade eyepieces later.


The larger the aperture the better. Don't worry about magnification.

Hint: find your local astronomical society, ask there, go to one of their "star nights", they may even have telescopes on loan.