What budget would be great in order to make a site optimized for mobile users?
Well it totally depend on the project at hand. If you are working on a simple site or a plain blog then only a couple of hundred bucks can get the job done. But if it is a large site such as an ecommerce site then it may take upto thousands of dollars.
The site is a travel blog. And contains several pages of various destinations separately.
I my opinion for a medium sized travel site, $300 to $500 is enough budget.
I think $500 to $800 will be just fine for a travel site.
I have done it for my local travel blog in our country. It cost me around $600.