I just found out I will be in Frankfurt and Mainz with a free Sat and Sun.
What should we do? I am not familiar with this area. Thanks

In Frankfurt, consider going to the Roemerberg, the old city center where the town hall is, then strolling down along the nearby Main River if the weather is good. The Roemerberg was badly bombed in the war, but has been wonderfully restored and is usually busy and colorful. Also near is the Zeil, the main shopping area, where often on weekends there is a food market with wine tastings. You could also visit Sachsenhausen, an old quarter just across the Main (accessible by footbridge) and have a glass of apple wine with the locals. I'm not so familiar with Mainz, but it does have a warren of fine old streets just off the main square.

As a matter fact, don't just plan to get a glass of apple wine in Sachsenhausen, but plan to make an evening of it. Most of the apple wine bistos are along the Schweizerstrasse, the nearest subway (U-Bahn) stop is Schweizerplatz. Tour the bistos, and then stop for a dinner and wine. You'll be sitting along long tables and benches and meet all kinds of fun people.

Get the heck out of Frankfurt for at least one day - one of Germany's most unappealing cities - at least in terms of fulfilling the romantic vista of Europe etched in your mind's eye - very modern city - one of few in Europe with several skycrapers - European financial capital, lots of sleek bank buildings. Does have vest-pockets of neat places aforementioned but lacks any real old-world feeling. Don't get me wrong, you could have some great two days there - lots of offer in its own way - but to see a more romantic Europe day trip to either Heidelberg, one of the few German cities not destroyed in WWII and a simply dreamy old-world looking city, or to the Rhine area - like to Rudesheim, cute though heavily tourist wine town on the Rhine, and take a boat ride through the fabled Rhine Gorge with the legendary Lorelei, to Koblenz, training or driving back to Frankfurt. Mainz too would be a more typical German city, but it too lost is old-world look in WWII.

I wouldn't bother much with Frankfurt. But if you do, Sachsenhausen is interesting (the apple wine is a bit like paint thinner, IMO.)

Heidelberg's old town is pretty much intact. It's okay.

But I think with two days, you could find a variety of scenery and city stuff by heading over to the Rhine. Mainz is a good-sized city with a small pre-war old town area (behind the main cathedral along the Augustinerstrasse) good for strolling and wine sipping, numerous pedestrians-only streets for shopping/eating, a couple of historical sights, and a gorgeous city park (with Biergarten).

You could spend a day or an afternoon there and another on an excursion down the Rhine (north of Mainz.) Braubach has a medieval castle you can tour - very cool - called the Marksburg. Bacharach is an attractive wine village with lots of half-timbered houses. Ruedesheim, Boppard, and St. Goar are attractive towns too. You could easily do the castle and another town in one day, and maybe squeeze in a river cruise as well (nearly every town is a boat stop.)