I'm not making any recommendations but there are a few companies that do cut grass. Even if they encourage you to sign a yearly contract, DO NOT for your first year here. We signed one with Mike's Maintenance. They do a lot of work for the Villages and residents. We have kept them for the second year because unfortunately, we couldn't find anyone who wanted to do a Courtyard Villa. Not enough money in it. I would also suggest to all newer folks, don't sign any continuing contracts for pest control, etc. until you actually look around and get a few estimates. There is Bates, Massey and Mike's that I know of to name a few.
Just take your time and if you won't be here often, talk to your neighbors who do move here full tiime and even to folks in other Villages neighborhoods to get some good information. Good idea is to drive around and get a look at how som work is done and then find out who does it.
Best of luck and Welcome!
