This may be controversial, but I am assuming your son lives in your house, eats your groceries, uses your water, etc.
So, if you feel comfortable doing so, I'd use that money to cover living expenses and the taxes, allowing you to safely invest the rest. If you want to understand a good portfolio allocation, google "three fund portfolio" and similar search terms. That way, one set of money becomes the living money, and the other set becomes the investing money. The general wisdom is to fund your own retirement first, before finding a college fund. There are scholarships and loans for college (and not all kids want to, can, or should attend a university anyway); there are no retirement scholarships. If and when you are stable, in part due to investing that money, then you can decide to set something aside to help with college.
You shouldn't invest money you are going to need every 6 months, so I wouldn't do that with the property tax money. If you have enough to float one or more payments, you could start a CD ladder, basically have a CD that expires every 6 months, so you take that out and put in the next one. Ideally, you could be several payments ahead so you could do 18 mo (or more) CDs, so you can get a decent rate. (For more info, google "CD ladder".)
And while it would be the gifter that pays the gift tax, it is still an important point. She can give money to you, to your wife and probably to your son as well. And if she has a spouse, he may also be able give money to each of you, in order to help stay under the cap. It wouldn't be your mistake to pay, but making sure grandma stays within on the right side of the IRS is a good idea. You can google "gift tax" for the limits and rules.