I mostly want a place for my husband and I to chill for a weekend. Budget $$. Privacy and scenery are most important.
There are lots of good options for private accommodation Hill Country, TX. I'm not exactly sure what "Budget $$" means as far as price range to you, but I see entire houses/villas/apartments in that area on airbnb.com . I would search by the dates you would like to go as the results vary a lot depending on what's available. Then use the filters to search "entire place" and the price range you were considering.
I would say the cheaper airbnb homes in that are $70-$80 per night, with excellent options in the $150-$200 range. Of course the sky is the limit on pricing.
There are also some great bedandbreakfast.com options that you can browse here.
Homeaway.com is another resource if you are more interested in an entire home or apartment. Browse the San Antonio region here.
I hope that gives you some good options to select from! Happy travels!