Hi,
I've used Track and Share for various general purpose logging reasons; it has built in options for mood etc. but quite customisable to form anything else be it numeric, text or categorical.
http://www.trackandshareapps.com/Pro
Developer is very friendly if you have requests!
If you wanted something with web sync, the nearest I know of is probably Tictrac. I haven't used it much yet, but I understand there is an app that can record entries offline, and then you would use the website for analysis. Originally I was slightly put off because I couldn't see that you could export data you logged onsite, but I believe there was a recent upgrade to enable that so thinking to look again!
https://www.tictrac.com