Here are some recommendations for price around $500:

1. Sony E 18-135mm F3.5-5.6 OSS:

   • Price: Within your budget.
   • Description: This lens offers a significant boost in both “reach” and image quality compared to standard kit lenses (like the 18-55mm and 16-50mm power zoom kit lenses). It covers a versatile focal range from wide-angle to telephoto, making it suitable for various travel scenarios. The compact design is a plus, and its superior optics result in sharper photos.
   • Consideration: If budget is not a constraint, you might also want to explore the Sony E 16-55mm F2.8, which is a fast zoom lens with excellent edge-to-edge image quality, although it lacks image stabilization.

2. Sigma 30mm F1.4 DC DN | C:

   • Price: Within your budget.
   • Description: This prime lens has a fixed focal length of 30mm, making it neither too wide-angle nor too telephoto. It’s a good all-rounder for travel photography. The bright F1.4 maximum aperture is great for low-light conditions and provides control over depth-of-field.
   • Consideration: If cost is not a concern, the Sony Carl Zeiss Sonnar T E 24mm F1.8 ZA* is another option. It offers a flexible 36mm equivalent field-of-view and performs well in low light

Also, the Tamron 17-70mm f/2.8 is another great travel lens for Sony APS-C mirrorless cameras.

I'm a big fan of compact primes for travel, so I'd suggest looking at the Sigma 30mm f/1.4 Contemporary DC DN or Sony E 35mm f/1.8 OSS. Fast apertures for low light, very sharp, and crazy tiny size/weight. Just pick your preferred focal length.

I took the Sony E 18-135mm on my trip through Europe and loved it. The versatile zoom range meant I rarely had to change lenses. It's not the sharpest wide open, but stopped down to f/8, it produced really nice images. And the compact size was perfect for traveling light. Definitely recommend it!