The Answer
$B$ visited on:
Saturday, April 21st, 2018.
Pairs and Dates
$E$ and $I$
Visited on Saturday, February 10th, 2018.
$D$ and $G$
Visited on Wednesday, January 24th, 2018.
$J$ and $A$
Visited on Saturday, March 3rd, 2018.
$C$ and $B$
Visited on Saturday, April 21st, 2018.
$F$ and $H$
Visited on Saturday, February 3rd, 2018.
Reasoning
$A$ not after $J$ but $28$ days after $F$ and $F$ didn't visit with $B$.
This tells us that $A$ cannot visit after $J$ nor before $28$ days after $F$ has visited. Thus the smart thing to do is to pair $A$ with $J$ since this is not technically after $J$ (which threw me off as I was avoiding the pairing until I read the phrase more carefully).
$J$ in March; at least $50$ days prior to $C$ on the same day of the week.
This tells us that $C$ comes after $J$ and that $J$ is in March. This limits the available dates for $J$ and $C$ to land on. $J$ is limited to the 1st and 11th, while $C$ is limited to the
$D$ and $G$ visited together, exactly $10$ days prior to $H$.
This statement is pretty obvious. With the follow on statement regarding $E$ and $I$ we know that $H$ is on a Saturday, and thus $D$ and $G$ visit on a Wednesday 10 days prior.
$E$ and $I$ visited together on February 10th and $H$ visited on the same day of the week.
This gives us a fully taken date, which is a Saturday, and thus allows us to understand that $H$ also comes on a Saturday.