Cuba: How to find "higher class" apartments, not just hotel rooms. AirBnB? Internet?

We (as two German tourists, with limited spanish language skills) are planing a vacation in Cuba for October. We want to cook for ourselves, so we are looking for flats with kitchen, not just hotel rooms.

Also, we prefer not to book the full vacation in advance, rather book each apartment a few days in advance, at max.

I know that there are a lot of private rooms for rent in cuba. However, I imaginge, most of them are quite rustic (5-20 CUC/USD class), which is not what we want. We'd rather like rooms as you can find them for 40-140 USD on AirBnb.

The problem with AirBnb we will probably face is the near to non-existant internet in Cuba.

I expect to have these options:

• looking for rooms/flats without internet by watching out for signs, asking locals, etc. I expect that this means to see a lot of rather rustic places, a lot of effort to politely decline rooms which are not really appropriate, etc. You may wonder why I find this to be an issue. But I expect some (polite) pressure here to accept a room, especially because a lot of the people on the streets work as promoters for rooms.

• booking via AirBnb in advance, from home. This would rip a lot of flexibility out of the trip.

• regularly hunting for internet in Cuba to book over AirBnb. I guess this is not easy, as the access is probably poor, and also the host's internet access is limited, so his answers will take longer as normal.

Are these assumptions realistic? Is it feasible to use internet on Cuba? I'd be happy about any advice...