The V & A and Imp War Museum are on different sides of the river but The County Hall Premier Inn is sort of half way between them really(right beside Westminster bridge). We've stayed there on a number of occasions and found it ideal. Not too long on the tube from Kings Cross, fairly easy to get to, and if you book at the right time you get get a reasonable rate. Just keep looking daily before you go as the rates change several times a day sometimes.
I'd stay at County Hall Premier too hc - great location for a stroll along the river bank in the evening too and a bite to eat or a spot of sightseeing.
Which station will you arrive at? Happy to help you with some directions etc.