Zillertaler Höhenstraße is closed in April. So are quite a number of hotels and cable cars/gondolas. April is not exactly a good time for a visit to the Austrian Alps - skiing season ends in many resorts after Easter holidays/early April and summer season doesn't start until mid/late May. In highest locations even later (Ötztal e.g.).

Zillertal is one of the mass tourism destinations in the Austrian Alps, some skiing areas are at high enough elevation so stay open until 11 or 18 April - thus you should find enough hotels and restaurants there. And then there's the glacier at the end of the valley which attracts skiers all year round.

I personally don't like April in the Alps because of the very limited number of things that are open and also because the weather is neither winter nor summer - and paths are often muddy, the grass more brown than green and so on.

Too bad you have already been to the Salzkammergut because that would be a better choice for April. Business picks up there at that time if the weather co-operates. And it is closer to Salzburg.

South Tyrol is the better option for April - Meran comes to my mind.