Saint Cross province is in the famous Patagonia. It is on the Argentine side, not on the Chilean.
If you want to plan your holidays there you should determine what type of activity you want to do. It can be split into various categories:
-Do traditional tours
If you do like trekking you should go to The Chalten town (it is 3 hours from The Calafate) and stay there your whole holiday. There were like 20 different ways to do trekking. The bad part is that the weather is awful: there is a lot of wind all the time and there is no good mobile phone signal (they only have got service with Movistar and Tuenti), this means that if you need to receive a SMS from your bank to authorize a withdraw and you use Claro, it will be hell for you. But who cares? If you do like trekking, you‘ll be happy.
Walk in cities
The Calafate is a really small city (not as small as The Chalten) but you can stay there a lot of days doing different things: go to lunch and dinner to a lot of restaurants, taste different meals with patagonic lamb and go to a good hotel with a great restaurant.
There you can contract different tours with a lot of companies: you can do a safari, go to the glaciers, do a kayak activity, and much more.
But if you stay there for more than 2 weeks I recommend you to go to other big cities such as Rio Gallegos and Ushuaia.
Do traditional tours
If you like to do tourist tours every day you can stay in The Calafate and contract the ones that you like, they have got like 100 different activities. There are dangerous (eg: do trekking on the glaciers) and easy (go for a safari)
If you like big cities and you value good Internet connectivity and having a lot of ATMs close to you, don’t stay a lot of days in The Chalten (or bring all the money in cash).
There are a lot of adventures to do in The Calafate and you can go to a close city to know more about the province.