Since you have access to a gym you may also want to consider doing some cross training on a bike, stairmaster, rower or cross-country skier.
You'll notice that most of the "modern" equipment has a monitor and different programs that will take you through different HIIT regimens.
Or you can just do your own - pedal/step/ski/row at a high rate until you feel winded, slow down for a time, then speed up again.
(Again you are mimicking the "play hard" for an interval nature of tennis, followed by a period of rest between points.)
While running is the most specific cardiovascular work out for tennis, some cross training is beneficial to work muscle groups other than the hamstrings that get the biggest workout in running - and to give a break from the pounding on the knees and hips that is intrinsic to running hard.
For instance the bike, stairmaster and rower will give your quads a better workout, and the skiier has more rotational movement with no joint pounding.
Still, since tennis is a running sport, doing the most work as running would be the goal of most - as long as it feels the body can take it.