Cozumel can be a cheap dive location, as well as a wonderful one. Depending on when you go, flights start at little over $300 total - cheapest in midweek usually, and the regulars on the Coz forum here love to tell others how to
do Cozumel.
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Being a single traveler can get pricey with hotels, but there are budget options, and using Orbitz vacations with
200entertain discount code can take $200 off of the package as long as your spend at least a week there, making a private room cheaper than a shared room at some hotels.
Be sure to uncheck the
Cozumel Roundtrip Airport Shuttle Service option as you can get the same van to the hotel and same taxi to the airport for half that if you pay there.

For example, Villa Blanca is a popular hotel with single travelers, close enough to town to walk it if your young and energetic, and you can get air, hotel, breakfasts and taxes for $653...

I think it was cheaper a month ago but these things change rapidly. Open Vacations on several tabs and try different dates.
That takes a big bite out of $1,000 I know, but it's really a pretty good deal. Scuba Mau is a more popular operator at the same dock as some others there and you can get 2 tanks dives a day for less than $60 trip plus tips - and you do want to tip well as the DMs work hard to please. Free shore diving on the house reef. Even with cheap eating, taking home food for the room fridge, etc, you'll go over your goal, but not much.
I presume you have at least the middle level DAN insurance. If your medical insurance would not cover you there or illnesses, I'd suggest trip insurance too, cheap at your age with other benefits.
Here is the one I use.