Looks like Weebly wins out as of October 2016. Take a look !
I would say Wix is one of the best out there, but it's my personal opinion. GoDaddy isn't bad either. You should probably do a little research on the web-builders and their pros and cons. Here's some info on that matter Best Website Builders, hope it helps!
Check out tecobytes.com , they are into UI/UX development. Mail them your requirements.
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