Finkenberg is part of the Zillertal Ski area (455km of runs) and is lift-linked to Mayrhofen. The two resorts are very different. Finkenberg is small, picturesque, has limited nightlife and après-ski and largely caters to the family market. Ironically, it doesn't have the best childcare, but the ski school and nursery slopes (when there is enough snow) are great for beginners. It also has the quickest access to the Penken area, which has absolutely excellent learner terrain. This can be reached by gondola, with minimal queuing. There is also one red run down to the village. For off-slope activities Mayrhofen is much better, while the skiing in Finkenberg largely favours intermediates and beginners. Experts really should go elsewhere for decent challenges beyond some off-piste. Finkenberg does have access to year-round skiing on the Hintertux glacier.
Overall, Finkenberg is a peaceful and relaxed way to get at the Zillertal region, without the hustle and bustle that you can experience in Mayrhofen.