For a rock fountain that does not flow into a pond, you have two options: You can find a fountain that contains the water within the structure of the fountain. This option is good if you don't want the hassle of installation. Another option that is becoming popular is to get a fountain kit where the water seems to disappear into the ground. What is actually happening is that a basin of water is hidden under landscaping stones. The water flows over the stones, into the hidden basin and is pumped back up to emerge from the fountain again. Kits like this provide lots of options for customization and integration with your landscape.
The ideal location for a pondless rock fountain is a flat area near a patio or other outdoor sitting area. You want it in a place where you can enjoy watching the water and listening to the babbling sound of it splashing down. If your proposed location is near an outdoor electrical outlet, that is helpful. If not, you should install a new outlet or hire an electrician to do so. Consider what type of rocks you will use to cover the basin, and how these will transition to the adjacent area of lawn or garden. You may want to edge the area with larger stones or landscaping products made specifically for edging, or just mulch the garden around it.
You may want to consider lighting so that your fountain is more visible at night. Some fountains have lighting built into the fountain itself. Or you can buy lighting made for ponds and waterfalls that can be installed at the base of the fountain, shining up to illuminate the water falling down. Another option is lighting made for general landscape purposes, which can be aimed at the fountain from a location distant enough to keep the lighting fixture dry. Plan ahead for the lighting option you want and make sure you have the electrical outlets necessary.
You have two options for installation: do it yourself or hire a contractor to do it. Some brands of fountain and waterfall kits certify their installers to ensure they are properly trained. Or the vendor where you purchase the supplies may be able to recommend someone. The vendor may also have a book or DVD that explains in-depth how to install the system if you want to do it yourself.
Water features such as a pondless fountain are virtually maintenance free, but there are some things you need to keep in mind. Water does evaporate, especially during dry seasons. Since your basin is invisible, you need to check the water level periodically. Move some of the rocks, or just pour some water over the rocks until you see evidence of overflow. If the water level in the basin falls too low, your pump can burn out. Remove the pump in the winter if you live in an area where the temperature goes below freezing. Take it inside where it will not freeze and re-install it in the spring.