The day "es" because it has certain features and properties as a whole or as a bottom line and not "está" because because it is or will be temporarily in a certain state.
Espero que hoy sea mejor
Espero que hoy será mejor
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You cannot use indicative in the second sentence because Spanish indicative, unlike English, requires the clause which uses it to be real or true or to be held as real or true. Otherwise, like when you introduce that clause -the "hoped" part- with "espero" to describe your expectations (notice "espero" is indicative because you "do hope"), Spanish indicative is not accepted then it defaults to Spanish subjunctive (that is why there seems to be so many "different" cases of its use).
Present subjunctive covers both present and future here.