Clifton is one of the university areas of Bristol. It's very lively, smart and full of bars, restaurants, open green space, clubs and shops and has great transport links. It's a fun place to live for young people and full of students. It's as safe as any area of a large city can be. It is VERY expensive, amongst the most expensive places to live in Bristol Lots of house shares around for students and young professionals.
Other areas nearby which are equally vibrant and have good transport links, are Redland, Clifton Wood and Cotham. Still pricey though.
A cheaper area a hop, skip and a jump away is Southville. A funky, vibrant area with good transport links, parks and a great theatre.
I'm Bristol born and bred. It's a great city. I hope your daughter has a fantastic time there and loves her new job.