Hotel in Vienna

In June of 2016, my wife and I will be on vacation in Vienna for a
week. Can someone recommend a hotel? We'd like one that is central,
near most of the museums, other tourist sites, and good restaurants.
If necessary, I'd be willing to pay up to 150 Euros a night, but I'd
prefer it to be closer to 100 Euros.

The hotel doesn't need to be luxurious, but it should be clean and
comfortable, in a safe neighborhood. And it should have an elevator;
we don't want to have to walk up stairs to get to our room.

It's not absolutely necessary, but I'd like it have free Wi-Fi.

I see that some hotels have air conditioning, but others don't. Will
we need AC in Vienna in June?