After the two of them stammered and said something unintelligible (they couldn't come up with anything) I told them I had some other important thing to do like watch the grass grow and politely declined their offer.

She also had a trampoline that killed a large patch of grass.

Find a group of investors in your geographical area, offer to do some sort of work for them, mow grass, haul away garbage, paint, whatever, and do it FOR FREE, for one weekend. 

The front yard was maintained but the back yard was over grown with weeds and uneven from their dogs digging holes and most of the grass dead.

Do a grass roots estimate for that (gross rents have nothing to do with that calculation).

I doubt you'll find "greener" grass as compared to your current investment.

hi john. thanks for the pictures. in regards to the rear patio and steps. look at the pipe coming out of the wall. it is in direct line with the worst part of the patio, where the lowest part of the patio is sinking. what you have here is water intrusion. the water is getting under the patio and sinking the base underneath. the steps are based on the patio so it is following wherever the patio goes. what you need to do here is totally tear up the entire patio, steps and everything. re-do the base and put in a new patio. first things first, you need to do away with the water source that is causing this. could be water from the roof, could be from that pipe sticking out of the wall right there. look at the path the water has left on the patio and the grass beyond it. you have a virtual river flowing there. that patio was designed to move the water toward the middle and funnel in into the yard. the problem is, the water is funneling toward the center of the patio but seeping under it and destroying the base. the new patio needs to have the highest point at the house and tilted toward the yard all the way across the patio at a 4 degree angle going FROM the house. that puts the water into the yard at a moderate pace and spread out across the entire patio. the front porch, same thing, you have water intruding underneath the porch and eroding away the base. find the source and reroute it somewhere away from the house. then rebuild the porch slightly tilted away from the house. 

Planting grass afterwords I doubt would really save any significant money in the project versas new concrete. 

Im thinking about offering to do the grass cutting and landscape maintenance as the landlord, and just looking for advice from other members. 

I'd consider xeriscaping by putting down river rocks, crushed gravel, or decomposed granite for a portion of the landscaping, as rocks are a lot easier to maintain than grass.