I am not sure how would you connect these to your TVs as most of them in the budget will come with RCA only. Do they still give RCA on TVs?
Regardless - check something LIKE THESE -
https://www.amazon.in/PreSonus-Eris...e=ps-sl-shoppingads-lpcontext&ref_=fplfs&th=1. (just an example)
This is a monitor with 4.5 inch mid/woofer driver, comes with BT so ease of connecting music directly & has the option to tweak the sound a little to your taste.
You can try and look for similar products - there are many companies that make them - from the pro world - it will be PreSonus, Mackie.
Form consumer world maybe edifier in this budget.