Ebersberg dates back to 934 AD when a cloister was founded here. In the Middle Ages and the Early Modern Age, Ebersberg was a famous pilgrimage place - people prayed (and pray) to Saint Sebastian (his brain pan is still in our church). Nowadays Ebersberg is a small town (12 000 inhabitants) and a really nice place to live!
The wonderful swimming lake Klostersee is only a 3 minutes walk away. Other nice lakes to swim in the area: Steinhöringer Weiher (small, fresh), Steinsee (near Moosach, small fee), Kastensee (with restaurant, small fee), Wiesmühle in Glonn (with very nice café/restaurant, pool with fresh beck water, small fee), Staudhamer See, Penzinger See (both near Wasserburg, small fee), Viehhauser Kiesgrube (park the car at the street near the railroad crossing, then take the small path).
Ebersberg forest: one of the biggest connected forests in Germany with a geometrical system of tracks; take a hike or a bike tour! There are two beer gardens in the Ebersberg forest, St. Hubertus and Sauschütt.
Munich is very near (40 minutes with public transport). My personal highlights are: church tower of St. Peter (Marienplatz), town hall tower, Marienplatz, Theatinerkirche (=church), Asamkirche, Viktualienmarkt, Zoo (named Hellabrunn), Olympic Park (1972), the English Garden, Nymphenburg palace and gardens, botanic garden, Residenz and Hofgarten (royal residence and garden), the Pinakotheken (4 famous art galleries, from the middle ages up to modern painting and design; http://www.pinakothek.de/en/home), beer gardens like Hofbräukeller (http://www.hofbraeukeller.de/der-hofbraeukeller/biergarten-muenchen.html) or Hirschgarten (http://www.hirschgarten.com/).
The beautiful area around the Chiemsee is called Chiemgau. It is hilly, small sectioned, rural with lots of lakes, always with the alps in background (http://www.chiemsee-alpenland.de/). King Ludwig II. of Bavaria built a pittoresque palace on an island in Chiemsee (http://www.herren-chiemsee.de/englisch/n_palace/index.htm).
The Bavarian part of the Alps can be reached within 45 - 90 minutes by car (or by public transport).
Other day trips could be to Regensburg (150 km): important town in Roman times up to the middle ages (seat of the German Reichstag), very nice city center (https://www.regensburg.de/tourismus/Home/3854); Passau (150 km): old, baroque town with 3 rivers uniting in (Donau, Inn, Ilz; http://tourism.passau.de/Home.aspx); Salzburg, Austria (110 km): old, baroque town (Mozart was born there; http://www.salzburg.info/en); Murnau (120 km): colony for artists since the beginning of the 20th century (Der blaue Reiter, Franz Mark, Wassily Kandinsky, Gabriele Münter, Alexej Jawlensky); Other palaces and castles from King Ludwig II of Bavaria: Neuschwanstein (http://www.schloesser.bayern.de/englisch/palace/objects/neuschw.htm), Linderhof (http://www.schloesser.bayern.de/englisch/palace/uebers/linderho.htm)