You really need two mics to do justice to a piano.
Your budget is cripplingly low to try to achieve this with any hope of quality.
Dynamic mics are really no good for piano, they're not fast enough, so straight away you're into phantom-powered condenser territory.
The thing about piano making techniques is there are as many as there are sound engineers. No one is 'better' than any other, but as you're going to be on a fairly limited setup - do you even have access to large mic stands or just regular 5ft with a 3ft boom arm? - let's forget any ambient configurations & go for a couple of simple close-mic options.
Small diaphragm omnis close to the hammers will really bring out the attack; spreading them maybe 2-3ft apart will give your stereo spread.
Large diaphragm cardioids can be used, but need to be further away; often set one left, near the hammers, 2ft in & 2ft or more up. The other at the sweet spot in the 'bow' of the body. Both pointing slightly towards centre.
Of course, if you don't know the mics, the room or the piano, there's a lot of room for experiment in either of those setups.
Personally I love a pair of B&K [DPA] omnis for the first config & either a pair of AKG 414s or Neumann U87s for the cardioids - however that's somewhere between 2 and 5 grand's worth of mic, so they're right out of the ball-park.
However, before you even start considering mics, you need a USB audio interface, capable of taking two mics simultaneously & with phantom power. This is going to set you back at least $70, leaving you $30 for the mics.
You can get a pair of 'large diaphragm cardioid condensers' for 30 bucks, but they're not going to be great.
I've experimented with the cheapest of the cheap, the BM-800 on vocals - & tbh, I've heard worse, but they'll win no prizes. I've never tried them on anything with such a high SPL as a piano.
I guess by now you've probably figured there is no cheap way out for this type of recording. Maybe you could rent a pair of decent mics for a couple of days, & a phantom power USB interface to go with them... but maybe it will come out more expensive than just hiring the venue's built-in system, which will presumably also come with an experienced engineer to handle it all - & presumably his fee is going to be the larger part of that cost. Piano miking is not something to try learn in a day, especially when you've a performance to think about.
 Made in China, zero quality control, apparently no two sound alike. You can find them under many different 'manufacturer' names on eBay, Amazon etc for 15 bucks each.