In reply to Godwin:
My absolute top tip: the Fußsteinkante (V-) in the Zillertaler Alps. Granit multi-pitch, some bolted belays and a few peg runners, otherwise natural gear. On the better pitches, which is most of them, like a less steep version of Bosigran but 500 m high! However, short glacier approach. No crevasses when I was there and Bergschrund unproblematic, but could have got worse over the years. The hut walk-in (Geraer Hut) starts from near a turn-off from the Brenner Pass motorway, by the way, so handy if you are on your way to the Dolomites anyway.
In the limestone pre-alps of Bavaria and Tirol your grade range of up to V+ is going to narrow the possibilities down a bit. The Schüsselkarspitze and Scharnitzspitze are almost on your way south (walk-in starts from near the village of Scharnitz, which you would drive through anyway), but here you are limited to:
at this grade. These are mostly bolted. You need at most a couple of bits of natural gear per pitch to fill in between bolts. Can be done as a long day-trip from the valley (walk-in three hours) or by staying in the Wangalm or Wettersteinhütte (both private, i.e. not German Alpine Club).
I've not yet been up to the Oberreintal (planning to change that this year), but the easy classics there are:
One recommended route on the edge of the Karwendl, and without the terrifying reputation of routes on e.g. the Laliderer Spitze, is the Ma-Ma Kante (V) near the Dammkar Hut. Walk-in starts from Mittenwald, day trip from valley.
[Just as an aside: the routes for which the Karwendl is best known are the Rebitsch / Spiegel and the Rebitsch / Lorenz on the Lalidererwand, plus maybe the Verschneidung (corner) on the Kleiner Lafatscher. Just count the number of UKC logs to see what the queues are going to be like on these.]
The obvious place to start in the Tannheimer Tal is the Gimpel south face. Possible as a day-trip from the valley; I stayed in the Gimpelhaus, a large and very commercial DAV hut... in fact near the bottom of my list of huts to go back to.
Also roughly in that direction: climbs on the Wolfebnerspitze, from a base in the Hermann von Barth Hut. Apparently nice climbs in the range 4 to 8 pitches, mainly lower grades. Three hour walk-in to hut.
One nice easy route just a few miles outside of Salzburg (which you might want to visit anyway) is the Barthkamin (IV+) on the Berchtesgadener Hochthron. Also mainly bolted with perhaps a couple of nuts or threads being necessary every now and again. Day-trip from valley.
I wouldn't recommend the Hochkönig (south of Salzburg) at this grade. The only easy route there is the Schluchtkante (IV) on the Torsäule, protected by the infamous Sigi bolts and even then only one per belay.