Taxis in most parts of the country seem to cost around �2 per mile. Your journey is around 7 miles, so I'd guess at somewhere around �15. For a quote, the Manchester Airport website advises phoning one of these numbers:
0161 489 2313 or
0161 499 9000
Alternatively, the number 18 bus runs every half hour (at 2 and 32 minutes past the hour) from Manchester Airport to Altrincham Interchange. It's about 10 minutes walk to the Cresta Court Hotel (or you could get a taxi from there).
Chris