Red River Gorge or New River Gorge?

Hey! I'm spending a month in Pittsburgh for work with my girlfriend in starting tomorrow. We will have 10 days off together and I wanna go camp and climb. Now, luckily Pittsburgh is within 4-6 hours from both New River- and Red River Gorge. My girlfriend is a beginner but already climbed 6a+, I'm not a strong climber myself, pushing it up to 6c/+ on a good day. We wanna climb some fun easy routes in grade 5 and 6, and I would love to try some classic routes in the 6c-region. Where should we go? Pro's/Con's between Red- and New River Gorge?  Any classic routes or crags we shoudn't miss? Any recommendations would be appreciated.