It sounds like you might not have the actual Mac that came out in 2011, but perhaps the previous one from 2007?
Lion Capable Macs (no longer supported)
If your Mac isn't new enough to run Yosemite, then unfortunately it's not capable of running an Apple operating system that's still fully supported. However, if your Mac has a Core 2 Duo processor (one of the models listed below), and as long as it has at least 2 GB of RAM and 7 GB of free hard drive space, it should still be able to run Lion (which, although increasingly less safe to use now, is at least better than Snow Leopard or earlier because it had been getting security updates until recently):
iMac (Late 2006 or Early 2007)
MacBook (Late 2006, Mid or Late 2007, or Early 2008)
MacBook Air (original model from Early 2008)
MacBook Pro (Late 2006)
Mac mini (Mid 2007)
Mac Pro (original 2006 model, including any bought in 2007)
Xserve (Late 2006 or Early 2008)
Still, 7 years of use is pretty darn good. You deserve a new computer. The mini/TV combination using your old mouse and keyboard is a good option (approx $600-800)
Another option: you don't need the absolute newest Mac, you just need a new-er one. Apple sells older and "refurbished" models on their site. Refurbished means Apple has certified them to be working, and may have minor cosmetic damage or may not even have been taken out of the open box. They offer their 1 year warranty on them.
https://www.apple.com/shop/browse/home/specialdeals/mac
Also, if you or anyone in your family are a student or an educator, you can get a discount on top of that buying through Apple.
https://www.apple.com/us-hed/shop
And they have their own refurbish prices:
https://www.apple.com/us-hed/shop/browse/home/specialdeals/mac
Or check out other sites:
https://www.macs4u.com/?gclid=CMqR4M3vndUCFZG1wAodoQ8H6A
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