If you liked A TREE GROWS IN BROOKLYN you might want to try one of these.
JOY IN THE MORNING - also by Betty Smith - is supposed to have a main character who is a lot like Frannie – I haven’t read it yet, but I will by the end of the summer!
BETSY AND THE GREAT WORLD by Maud Hart Lovelace is about a young girl about the same age and era as Frannie who is traveling alone in Europe just before the first World War breaks out.
ALL OF A KIND FAMILY by Sidney Taylor is written for elementary/middle school aged readers, but is a very interesting and funny look at another part of New York's immigrant community during this time.
I just picked up BOWRY GIRLS by Kim Taylor - it takes place slightly earlier than A TREE GROWS IN BROOKLYN but deals with poverty in New York and is very good, so far.
I CAPTURE THE CASTLE by Dodie Smith takes place a little bit later and also in England, but it is a very funny story of a family trying to hold itself together in the face of poverty and an ineffectually, whiny father. (Sorry, a little judgmental of Johnnie again...)
DADDY LONG LEGS by Jean Webster is the hilarious story of a girl who is raised in poverty in an orphanage and is sent to college by a mysterious benefactor.