Belarus Station, the Moscow terminus for trains to/from Belarus (Minsk and Brest), Kaliningrad, Smolensk, and international destinations including Vilnius, Warsaw, and Berlin, is very close to the Brighton Hotel (less than 5 km by road).
By taxi
Depending on the time of day, the journey by taxi should take around 15 minutes, and should not cost more than $20 if you negotiate a fare on arrival. For greater security and comfort, you can book a transfer with a driver to meet you off your train here.
By metro
Take the dark-green line from Belorusskaya Metro Station (accessed from the mainline station concourse) and travel north one stop to Dinamo. It is around 20 minutes' walk from there to the Brighton Hotel but you can also use the hotel's complimentary shuttle service if available.