There is a place down Veal's lane in Marchwood which I think still does livery and has an arena. There is also Ipley Manor which is a 10mins drive but has hacking direct on to forest. There is also Decoy pond which is by Beaulieu Road Station and is around a 15 min drive but again has amazing forest hacking.
If she has got the money then def go for Ipley Manor or Decoy Pond. I grew up in the New Forest and lived just past Marchwood and we had 5mins roadwork and had to cross Marchwood bypass to reach New Forest and then could hack all day long! Nobody would want to cross the bypass on horse now as it is so busy!
I wish I could move back as Staffordshire hacking is rubbish in comparison