I have only one day to visit Hallstatt and weather predictions are good. I looked into the things to do, but they sure know how to boost up the prices (but that's another topic discussion)...
Going to the mine is 24 euros, visiting the mountain is going to cost me quite a bit too. Since I only have one day and I don't want to rush anything because of having to pay quite some moeny for it, what do you recommend as a highlight of this WHS?
Also, are there walking trails starting from the mine?

If you have only one day in Hallstatt, I would skip the trip to the Dachstein massif and would recommend to visit the town and the salt mine, and perhaps a boat trip. These are the essential parts of the WHS. However, I didn't know that a ticket to the mine is so expensive today. I remember when I was there several years ago, it was cheaper.
You can hike from the town to the salt mine and back on an alternate route. It's a nice walk with many beautiful views.
I found no description in English, only two in German:

http://www.hallstatt.net/ueber-hallstatt/wanderzeit/wandern-hallstatt/welterbe-rundwa nderweg/

http://www.hallstatt.ooe.gv.at/gemeindeamt/download/219717986.pdf

The trail along the eastern shore of the lake is also very nice.
However, a trip to the Krippenstein summit is also worthwhile, the view over the lake and the mountains is magnificent. But if you're there at the Pentecost, there will certainly be a long queue at the cable car station.

Make sure to visit the World Heritage Museum:
http://www.museum-hallstatt.at/
It's not expensive and very worthwhile. It makes clear why Hallstatt is important and exhibits the major finding from the Hallstatt Culture.
According to the following website you can spare 6 Euros from the entry fee to the mines by not using the cable car opting for hiking instead:
http://www.salzwelten.at/salz/images/stories/hallstatt/sw_ht_tarifplan_2012.pdf