Hello Mark
Welcome to the forum. I'd suggest you check out some of the towns just outside of Frankfurt. Wiesbaden or Bad Homburg, for example. As you mentioned spa town, one of the best in Germany is Baden Baden. Its about one and a half hours from Frankfurt via high speed train (taking this train, called the ICE, is in itself a very German experience)and they leave every hour from the airport train station.

For accommodation, perhaps a smaller type of Bed and Breakfast which you'd find outside of the major cities for the vicinty of 60 to 80 euros. These of course won't offer airline discounts.

If you opt to stay in the Wiesbaden/Mainz/Frankfurt area a recommended day trip is a boat cruise along the Rhein River. Its nice scenery, although its more appreciated in spring or summer.

As to flights, ex ORD, both UA and LH are open in all classes. You seem to be quite enthusiastic about flying first class.I don't know which airline you work for so can't say much about the agreements. If its a Star Alliance carrier, you can purchase an ID90 eligible for a LH first class seat, space available. But the ticket must be designated for first. Don't know what UA's policy is as regards F/class upgrades from an ID economy or business ticket.

The return flights FRA-ORD are looking a bit tighter, though I suspect they'll go out with a couple seats free. The best bet is the UA 8:30 am which as I understand it, is a non revs dream flight. The downside is the early departure.

Hope the info helps.