Rigi or Titlis in Switzerlands
 

Planning a 3-day driving trip each in Rigi and Titlis, in mid-June, will appreciate any experienced advice. Your choice of hotel recommendations will be appreciated.
If I have extra 3 days, what would be your choice (nearby driving)?

Unless you have done them before, I would suggest the Jungfrau and Schilthorn if you have another 3 days. You could drive to either Lauterbrunnen or Grindlewald.

Yes to the above. Cars are not allowed above the floor of the Lauterbrunnen Valley. I suppose there is a way that a vehicle might be driven to Wengen, but I don't know what it is. Transportation to the Schilthorn and to the Jungfraujoch is available from Lauterbrunnen.

Engleberg from Luzern by rail is about one hour and then after a short walk you reach the cable ways going to the top of Titlis. Do not beleive there is a hotel atop Titlis, however there are many within Engelberg as well as a casino.
Rigi can be reached by rail from Vitznau via the Rigibahn and from Arth-Goldau via another rail. There is a hotel atop of Rigi, the HOTEL RIGI KLUM
Did stop at this hotel for one night, however it was very cold and decided not to stay the night due to the lack of heato has a large ristorante. There is a beautiful view from Rigi on a clear day and the sunrise must be a must. On the other hand, you can reach
Weggis which is on the lake side of Rigi and you might look into the Hotel
ALBANA, appears to be a very excellant choice for a stay.
For your extra three days would take
the Jungfrau, Schlithorn and possible Grindelwald First. All worth the ascent on a clear day... Richard of LaGrange Park, Il..

Rigi is wonderful, but I don't know what you mean by a 3-day driving trip there, unless you mean the environs surrounding the base of the mountain. You certainly cannot a car up the Rigi.
At Rigi-Staffelhohe (about 3/4 of the way up from Vitznau) the Hotel Edelweiss very nice with good views and food, but I have not been there for a few years. If you stay there, ask for a south-facing room in the newer section.

I have stayed at the Hotel Alpine Flora in Vitznau and liked it. It's within walking distance of town, although having a car helps after dinner in town.Quite a number of rooms overlook the Vierwaldstaettersee. It offers some walks in the surrounding property. The food at the hotel was good, but not exceptional.