Where are you comparing prices for the cards? You might try using PCPartPicker if you are in the US, or another country that the site supports (see the drop-down list to the upper right of the page). For example, in order of relative performance...
GTX 1660:
https://pcpartpicker.com/products/video-card/#sort=price&c=439
GTX 1660 SUPER:
https://pcpartpicker.com/products/video-card/#sort=price&c=450
GTX 1660 Ti:
https://pcpartpicker.com/products/video-card/#sort=price&c=438
RTX 2060:
https://pcpartpicker.com/products/video-card/#sort=price&c=436
RX 5700:
https://pcpartpicker.com/products/video-card/#sort=price&c=445
The 2060 and 5700 might be slightly over your budget, particularly after things like tax are figured in, but you can sometimes find certain models on sale for around $300 online.
As for relative performance, a 1660 SUPER performs just slightly behind a 1660 Ti, while typically being priced closer to the original 1660. The original 1660 should perform about 10-15% slower than those cards, a 2060 will be about 15-20% faster than them, and a Radeon RX 5700 will typically perform another 10% faster than a 2060. The 2060 also has hardware to support raytraced lighting effects in the handful of games that support them so far, though even with dedicated hardware they cause a big hit to performance when enabled, so it remains to be seen how beneficial that feature might be in the long term. I suspect that graphics cards released a year from now will likely support raytracing a lot better, seeing as it's apparently going to be a standard feature on the next generation of consoles.
AMD is also expected to be launching an RX 5600 XT in the coming weeks, with performance likely somewhere above a 1660 Ti, but below a 2060 on average. I'm not yet sure about the exact dates those will go on sale, but they will likely be announced at CES within the next couple weeks.