Things to do in Tegernsee area?

I will assume your trip is Spring to Fall? Drive south into Austria to the Achensee about an hour drive (lots to do there): https://www.achensee.com/ In Maurach take the cable car to the top of the Rofan and walk to the Dalfaz Alm: http://www.dalfazalm.at/ Other things to do on the Rofan too: http://rofanseilbahn.at/sommer/ Go to Pertisau and into the Naturpark Karwendel: https://www.karwendel.org/ From Maurach drive another 45 minutes south and you are in the middle of the Zillertal at Mayrhofen and "echt" in the Alps: https://www.mayrhofen.at/en/ From Mayrhofen drive another half hour southwest and you are at the Hintertux Glacier: https://www.bergfex.com/hintertux/webcams/c256/ snow! This is a little aggressive for a three year old and can use a day or more, but don't discount it...

Many possibilities, e.g., ...

Sights:

• church of the former Benedictine Abbey in Tegernsee (historically one of the most important Benedictine abbeys of Europe);
  • trip to Kloster Reutberg (ca 20min; baroque church, very nice Bräustüberl for lunch); the nearby Kirchsee is shallow and ideal for children
    
  • Dietramszell monastry
  • Benedictine Abbey Schäftlarn
  • Buchheim Museum in Bernried at lake Starbergersee (modern art)
  • Chiemsee (ca 40 min; boat trip to Herrchiemsee palace and frauenchiemsee abbey)

Nature and (easy) hikings:

• boat tour on lake Tegernsee
• tour the Hirschberg (easy, fine view; starting point is Scharling)
• hike from Tegernsee over the Baumgartenschneid to lake Spitzingsee (back by bus who runs through the forest several times per day);
• easy hike to the Königsalm (most convenient starting point is the "Winterstube" parking on B 307 SW of Kreuth), can be extented (with sturdy shoes) to the Schildenstein mountain
• lake Schliersee and cable car from Osterhofen up to the Wendelstein (if you plan accordingly, you can descend by cog railway on the opposite (north) side and take one of the two afternoon buses back to Osterhofen).
• trip to the Walchensee; take the Herzogstandbahn cable car up to the Herzogstand and walk over the ridge to the Heimgarten (spectacular views on both lakes and the alps)

... and many more.

• First, make sure you utilize the excellent tourism website for Tegernsee and do not hesitate to contact the tourism office for suggestions. If you can, use the German language site and not the English one as it will give you much more info regarding activities around your planned holiday dates.
• Also, don't forget to get a TegernseeCard from your hotel. They offer free travel on the buses around the lake, discounted tickets on the Wallberg cable car, 2 free boat trips per day, and other discounts.
• Rent bikes and ride on the path around the lake (22km) stopping where ever looks nice. We rented electric bikes from Tegernsee Bike in Bad Wiessee, they were extremely helpful and even gave out group a beer and schnapps when we returned our bikes that evening.
• Take the cable car up to the top of Wallberg and hike to the nearby Wallberghaus for a beer and some food.
  
• Drive out to this parking lot and hike your way to Almwirtschaft Siebenhütten
• Drive one valley over to Schliersee and visit the Markus Wasmeier Freilichtmuseum, a very nice folk museum.
• Drive to Koster Reutberg for good beer and excellent food. It's like a mini Andechs but without tour buses and better food. Take a walk in the nearby countryside after your meal or drive to the nearby Kirchesee for a swim.

Hope this helps,

DJ

We are traveling with 2 boys ages (5 and 3)

This changes things a little. I would say skip renting bikes then but the rest are good for small children (the Markus Wasmeier Freilichtmuseum is not to be missed with kids).

Additionally I would add the water park in Bad Wiessee if you children are good swimmers, the wildpark in Blindham about 40min drive from Tegernsee, feed some duck/geese,swan on the lake, a day trip driving through the mountains to nearby Mittenwald would be nice as well.

DJ

If you did not have the kids (or could find a babysitter) then I would recommend the Monte Mare Seesauna. An excellent bath experience with a more diverse, and younger, crowd than the baths at Baden Baden (it is co-ed and nude)

Otherwise, do enjoy a meal and some excellent beer at the Herzogliches Bräustüberl Tegernsee.

I could add more...but it would be a repeat of what others have said.