I'm a Julia and really like my name - it's quite classic/timeless yet not overused (I've only met a couple of others in RL and they were very different ages to me). It's also easy to say and spell and very international. Only issue I've ever had is fairly minor - occasionally some people (usually 60 plus) will automatically call me "Julie" instead, but it's not a big deal.
Alice is also lovely - also very classic/timeless, although a lot more popular than Julia (so it's possible she may not be the only one in her class if that matters).
Cici is very cute - as a nickname. Sorry but I think it's a bit insubstantial sounding as a given name, although Cecilia, Cecily etc are very nice (or use another C first name, with a C middle name to get Cici?)