Personally, I would stay on the train until the main station (Gent Sint Pieters) and take tram #1 from there. Get off in front of the Gravensteen (castle), from there it is a 2 minutes walk to you hotel.
I would hesitate to count on a taxi from Dampoort for two reasons: I do not think that there are always taxis waiting there (it is a small station) and the taxi will have to go around the city centre to get to the hotel.
On the other hand, a taxi from Dampoort should only cost 8,50€ (which is the base price that includes the first 3 kms).
A taxi from Sint Pieters station (where there are taxis waiting for sure) should cost between 10 and 15€.Edited: 23 May 2017, 06:18
Well, the cheapest way would be to walk from Gent Dampoort, which at almost 2 km, would take me about 30 mins.
But indeed if you look at the map on your hotel's website, the closest tram stop to it is Gravensteen, which means the easiest route by public transport would be tram #1, direction Evergem/Wondelgem, and that means getting off the train at Sint Pieters station, and taking this tram from stand 2 (where there are ticket machines and at the end of the platform, the De Lijn ticket office: cost buying individual ticket is €3 or you can buy a 10-trip Lijnkaart for €15). Here is where to find tram/bus stops outside the station: https:/…20Sint-Pieters (NB theoretically it is also possible to take tram #4 but this route has so many different variants - most of which DON'T stop at Gravensteen - that I would suggest sticking with #1). When you get off at the Gravensteen stop, keeping the castle on your right, walk across the Rekelingestraat bridge and Jan Breydelstraat is the next street on the left.
That said, if you really want to get off at Dampoort station, and not to walk from there, from outside that station you could take tram #3, direction Mariakerke Post (from stand 13), or bus #38, direction Blaarmesen (from stand 1 or 3) just 4 stops to Korenmarkt. From there, it's just one block to Graslei (on your right, looking back the way the tram came), from where you walk across the bridge to Korenlei, and turn right into Jan Breydelstraat. Here is the map of tram/bus stops outside Dampoort station: …delijn.be/files/attachments/.3152/Perrons_G…
We took a taxi to the Gravensteen, then took the tram to the station for the return trip. Once you get your bearings in the city, it is easy to use public transportation. Down load the city maps to your smart phone before you go for use without internet connection once you get there. This is very helpful when you use public transportation and want to know when to get ready to get off the tram, bus or train. I also "pin" important locations on the map ahead of time (i.e. hotel, train stations, museums, etc.) for easy navigation.
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