I would recommend the Melrose/Girard estates or passyunk areas. Very deep in south Philly and old school but still nice and clean and safe feeling. Lots of families and dogs. We have a couple (M/M) across the street that moved from Asbury park and like it here. Not close to the trail but running at FDR/ the navy yard is a possibility. You would definitely be able to get a house for under 425k. I bought a 3 bed 1 bath rowhome in 2021 in Melrose for 260k. Good luck!