Morelia is a very attractive city so it would be a pity not to schedule time there. The airport is quite a long way out, and on the opposite side of Morelia from Pátzcuaro.
I have stayed twice at the Hosting House Congreso, which is superb value for money. If you use the search function, you will find my review.
I've stayed at and recommend Hotel Horizon which is located on the eastern side of Morelia (the airport is northeast and WAY-OUT of the city) which is an easy enough drive/taxi ride away. The hotel offers a decent complimentary breakfast and there is a fee for their airport shuttle if needed. But the location seems great for your situation of getting to your hotel sooner than navigating through or around the city with your late night arrival. There are a number of other chain hotels located on the same street.
Is it safe to travel to the state of Michoacán ?,( Planning a trip ) all you hear is violence in the state, is it safe for a couple to travel to Mexico .is it better to rent a car or just ride on a Taxi or by bus ?
Don: I am sure there are no-go areas in Michoacan, which is Mexico's largest state, but the inter-cartel violence is not likely to impinge on you as a tourist, who is unlikely to visit those areas anyway. As anywhere, if driving, you are more likely to be the victim of opportunistic theft, a shakedown by protestors or the police, or a road accident. That said, I have been driven by friends to Morelia, Pátzcuaro, around the lake, Uruapan and down to the coast on several occasions. The only incident was when protesters took over a casa de cobra on the toll highway and we paid our toll to them rather than the authorities. I have also travelled around b y bus without incident. Long-distance buses in Mexico are of extremely high quality (way beyond Greyhound) and security on them is tight these days. Just google the subject and you will find lots of photos. Taxis are widely available even in smaller towns, as locals use them a lot too. Uber is available in the bigger towns and cities.