Does the Tucson,Az VA hospital have a place for out outipatients to stay ?

I would call and ask. It really depends on what the outpatient treatment is for

Some VAs have a hoptel if someone is getting daily treatments like radiation that don't require inpatient stay. Other have domicilliaries or residential programs if it is outpatient psych or substance abuse

At the very least they can refer you to a local hotel. If you stay at a hotel, let them know you are a vet or retired military and sometimes you can get a substantial discount