There is a lot of free web hosting solutions (just google it), however they all offer limited features.
If you don't mind shelling out a few dollars or euros a year, buy a domain for yourself; then purchase some cheap web hosting solution, these usually are about 4� or something a month. That'll cost you about 60� a year and you can do all kinds of things with your web space. (MySQL database, PHP for any server side code etc.).
Just my couple cents on best place to host Construct game. Nothing is stopping you from using one of those free web hosts, however, but do closely inspect their features first!