Between Varenna and Stresa

The drive from Varenna to Stresa is not a long one. However, either Lugano or Bologna have much to offer.
Locarno is also on Lake Maggiore like Stresa although in Switzerland instead of Italy but not as different as your two other choices. Lugano felt more "polished" and upscale to us.
We loved Bologna and would consider staying there for an extended time. The surrounding area is interesting too with all the food producing towns.

I should mention I'm traveling by train.

You can still do Varenna to Stresa by train and boat.
The quick way is to go via Milan. This is a V-shaped route. If you want the direct route, this is more complicated and will take longer but may appeal to you:
1) Ferry from Varenna, across Lake Como, to Menaggio.
2) Local bus Menaggio (IT) to Lugano (CH). Lugano is worth a few hours, it is a "sophisticated" city on a lake.
3) Train Lugano to Bellinzona. Bellinzona has three castles which are a world heritage site. Info and a video here: https://www.ticino.ch/en/itineraries/details/The-three-Medieval-castles-of-Bellinzona/138309.html
4) Train Bellizona to Locarno. Locarno is at the north end of Lake Maggiore.
5) Lake boat along Lake Maggiore from Locarno (CH) to Stresa (IT).

You could stay overnight in Lugano, Bellinzona or Locarno.

Frank II,

Another route you might enjoy is....

• Train Varenna to Milano Centrale and from there to Domodossola
• Scenic Cento Valli Railway from Domodossola to Locarno (the station for that in Domodossola is underground so you may not see it when you first arrive there).
• Spend at least one (and preferably two) nights in Locarno. It's an incredibly beautiful city (IMO) and very posh. There's a Casino there as well. While in Locarno you could visit the historic Madonna del Sasso Franciscan Monastery or take the Cable Car up to Cardada & Cimetta. As I recall, there's a hotel right at the top of the cable car station with a patio overlooking the city - great place to have a cool one and a fine hot meal while watching the Paragliders sail by. There's also a platform near the hotel that extends out over a cliff and provides great views.
• Following your visit there, take the Ferry to Stresa. It's a very pleasant and scenic trip, and the Ferry stops at many of the towns along the lake.

I've heard that my family originated in that area, so it has a special appeal for me.