"Would you suggest spending 3 nights in the Rhine Valley then heading to another location in Southern Germany for 4 nights or vice versa?"
Welcome to the forum.
A week will go quickly. You arrive on May 29 (right?) after a transatlantic flight (right?) Most people find their inner clocks are all messed up and don't accomplish much on Day 1 - they get to their first base, freshen up, settle in, have a meal, maybe see a few things perhaps. So it's best to plan for just 6 days, IMO.
If you travel to Munich on one of those days, much of that day will be given over to the logistics - a 5-hour train trip and again the checking in routine - so you lose close to half a day there.
A trip to Florence from Munich will later snap up 8 hours altogether using the above EC 85 connection - so most of your day.
So what to do? First, congratulations... You've selected one of Germany's most beautiful and diverse areas for your first destination. Rick Steves tends to fly through this region on his tours and in his videos, but you don't have to. There's a ton of things to see and do in this region - Roman historical sites, WW II history, medieval castles, open-air museums, awesome cathedrals, half-timbered old-world villages, river cruises, outdoor activities and more. With 10 days I might send you to Bavaria. But with 7 I would spend the 6 full days of sightseeing you'll have within the rough triangle formed by Trier, Mainz, and Cologne.
Sam has given you a good tip for Rhine area transport passes (there are a few other passes too.) The train transport in this region is scenic and outstanding along the Rhine and the Mosel Rivers, where tracks follow the river in most places (and also along the other Rhine tributaries.) You won't feel like you're wasting your time on these trains.
I agree with Nancy - flying to Italy is smart. FRA and Cologne-Bonn airport (CGN) have direct flights (Germanwings from CGN.) The point IMO is to enjoy the train trips where the train trips are enjoyable (like the Rhine and Mosel River) but don't waste time on excessively long train rides (like the one from the Rhine to Florence, via Munich or not.)
Here are just a few great places that you might have escaped your radar:
MOSEL:
Cochem
Falconry show at Cochem's Castle
Cochem's main square
Trier, main square
Trier, UNESCO sites
Burg Eltz
RHINE: Rüdesheim's Seilbahn and Rhine Castle Trail
REMAGEN: WW II Bridge at Remagen museum
BAD SOBERNHEIM: Open-air museum
COLOGNE: Cathedral, museums, including Gestapo prison/Nazi Doc Center