I know at $90ish this is more than you indicated you wanted to spend, but I have an earlier version of this Bissell Steam mop. It's great on tile and really saves my back. Best of all , the only thing you have to put in it is cheap distilled or purified water.https://www.amazon.com/Bissell-Sanitization-Flip-Down-Scrubber-1940A/dp/B0091YYUAM

I know there are other brands and probably a cheaper price point; do a little searching. :-)