Answer
$4$ days in San Antonio and $3$ days in Dallas.
Work Step by Step
Assume the number of days spent in San Antonio is $x$. Then the number of days spent in Dallas is $7-x$. Then our equation is: $275x+(7-x)400=2300\\275x+2800-400x=2300\\-125x=-500\\x=4$.
Thus we should spend $4$ days in San Antonio and $3$ days in Dallas.