Can someone tell me if visiting Qobustan-Mud Volcano-Astegah-Yanardag is good for 1 day?
Can we do it with taxi? And how much that will cost?
Go to this place you can visit a lot of places. Rather than take a taxi why you do not try to walk or car hire people here to experience
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Yes, visiting all places is possible, will take you whole day though. Certainly the car would be needed as places are scattered around Absheron peninsula. Gobustan & Mud volcanoes is 60 km away from Baku. Car would cost around 150-200$, but you will need to make sure that the driver knows all the places as most taxi drivers would not know them for sure. It might make sense to approach travel agency to provide you with the driver&guide. IT should not cost more than 200$, taking private taxi would cost less (in the region of 100-120$) but you might end up losing a lot of time searching for the places.
These places are in the opposite direction. The mud volcanoes and petroglyphs are south of Baku, whereas the fire temple and gas crater are east of the city. It is technically possible to do as 1 day, but it's a loooooong day.
As mentioned, while Baku drivers can easily get to Gobostan, getting to the mud volcanoes is a little more complicated. They are not accessible by road (off-roading required) and they are not sign posted. Many Baku based drivers do not know where they are and you end up wasting a lot of time driving around trying to find them. You could have the bus/taxi bring you to Gobostan, then get in a local taxi who will know where to go. Of course, having 2 drivers will be more expensive.