I use starhopping on my altaz mount - from a map. I have the Orion SkyView and for casual observing at low to medium power its fine. As for a map I use StarMap Pro on my iPhone, or Sky Atlas.
Some mounts - "push to" - have digital setting circles (Argo Navis or Sky Commander, you decide what you want to look at and the controller tells you which way to go to get there - you push the scope.
And yes there are "goto" altaz mounts like the iOptron Cube and the latest one-arm fork Celestron has with a C6 on it; Skywatcher is also selling a small one arm fork with a 90mm Maksutov on it (rather small).
Most of these require calibration using the two star method to achieve accurate "goto"s.
Personally I think it is worth taking the effort to star-hop from a map for two reasons:
a) you will learn your way round the constellations. I am constantly disappointed by people who are so used to goto scopes they have no idea where anything us, or what else is nearby.
b) using a map you can see what else is nearby at a glance. Worth knowing IMHO.
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