Hotel Suisse (Place de Cornavin 10)

First off, June 30 is a pretty long ways off, so a lot can change.

Second, you don't say what your priorities driving your choice of hotel location
are, but if you are willing to stay near the airport, you can save a fair bit of $.

Don't forget that you'll get a voucher good for all local transport in Geneva
and the airport is a 7 minute train ride from Cornavin.

Priorities are near the train station so we can drop our luggage at the hotel and do some sightseeing (old town, UN). The Hotel Suisse is $313, which is more than I expected but less than others near the train station or near the airport. Also near the train station so we can hop on for the 7-minute train to the airport the next morning.

The Ibis Geneva Aeroport is $181 all in for that night as of now (and has AC).

You can decide if staying near the airport with the extra overhead of going
there to leave your luggage is worth the cost savings.

Alternately, there is obviously going to be a left luggage option at the train
station. Leave your bags there, see the city, then go to the hotel.

Finally, your dates are far out enough in time that some hotels, especially
the individually owned ones, may not have finalized their prices for next June
yet.