Many travelers around the world are on business and require VPN to securely access their corporate networks. Hence, hotels tend not to block VPN. Even on a 2-week vacation in different China cities, I only stayed in 1 hotel (in Shanghai) that blocked VPN, which I bypassed by choosing a different VPN server IP.

Once you are connected through VPN (you may have to clone your MAC onto the router), they should not be able to perform deep packet inspection on your data, nor OUI and TTL within the tunnel, nor multiple connected devices.