I've stayed at Ararat Park Hyatt many times. It is definately one of the nicest hotels in Moscow, many would say the nicest. Located across from the famous Metropol and adjacent to the Bolshoy Ballet. Rooms are quite large, and very nice. I doubt you will be disappointed with this hotel. Within easy walking distance to at least 3 or 4 Metro stations. I would suggest that the only view rooms would be those facing West, and overlooking the Bolshoy Teatr. I would say that you will need to be at levels 6-9 to get the best view. Security is very good. Key access to levels 3-9 elevators. Sushi Restaurant on 1st floor is quite good. and one of the best views of downtown Moscow/Red Square is from the 10th floor Conservatory Bar. The breakfast is not bad and there is a fitness center on I think the 5th floor??
All and all it is a great hotel. Has recently been added to American Express Fine Hotels and Resorts for 2004. I've stayed there a few times when Hotel was full, and did not get upgraded, but more often than not, I have been upgraded.
Regarding the queston on Saint Peterburg. I have stayed at a few hotels. The most bally-hooed hotel and my reputation the top hotel is the Kempinski Grand Europe Hotel located on the Nevsky Prospekt. It is quite nice. I think the Asoria is getting rave reviews lately. Also, the Radisson SAS is quite nice. I can not imagine you will go wrong with any of them.
btw, regarding transportation costs from airport to Park Hyatt, I think I pay about 1000 Roubles from SVO to the Hotel with a private driver. Not sure what it maybe from DME.