Quite a few bread/pizza makers go the unglazed quarry tile route. It can be used to make great NY style pizza, but not without a few caveats.
Out of all potential stone materials, there's nothing less thermally conductive than tiles. What this means, is that, in order for proper bottom browning and respectable bake times (less than 7 minutes), you're going to have to pre-heat the tiles to at least 650 deg. f. In an oven that may only go to around 550 on the dial, this means tricking it to go higher. This can mean things like cutting off the lock for the cleaning cycle or covering the thermostat probe with ice. As long as you're conscientious, oven hacks are perfectly safe, but there's always a little risk involved (more to the oven than to the home).
Another aspect to the oven modding equation is that, as you remove the thermostat from the picture, there's no way to reliably ascertain the temperature of the stone without an infrared thermometer, so your very inexpensive quarry tile solution just got a bit more costly.
If you want great NY style pizza without oven mods, then you have to turn to more conductive stone materials. The reigning champ is 1/2" thick steel plate. An 18 x 18 x 1/2" slab could run you from $40 to $70 depending on your local sources. Compared to the <$6 price tag of quarry tiles, $70 is a tough pill to swallow, but I think it's important to remember that this $70 expenditure is giving you the ability to replicate the results of pizza ovens costing thousands of dollars in a home oven.