Hi Taoliver,
There are some very good local options in Houston for memory foam mattresses and they are listed in post #2 here.
If for any reason you decide to buy online then some of your better options are listed in post #12 here but I would personally only go in this direction if an “apples to apples” comparison was in the range of 20% to 25% less (as a rough guideline) than a local purchase because of the additional risk of purchasing a mattress that you have never tested. The actual percentage that each person may use as being roughly equivalent value would depend on the individual and would depend on their “risk tolerance” for an online purchase and any return or exchange options that was provided by an online merchant.
Your budget is plenty for a good quality memory foam mattress IMO and I would talk with each manufacturer or retailer you work with so that they can help you know more about the specific types and quality of the materials and layers they use and how well their mattresses will meet your criteria.
Phoenix