Quick note - After rent and utilities ($1,250) split the remaining $1,650 roughly as: $350 groceries, $120 transit, $150 fun, $100 sinking fund, $50 household/cleaning, $700 to emergency savings, leaving about $180 for phone/internet or as a cushion but then once you hit about 3 months of essentials in the emergency fund, drop that to $300 and roll the extra into sinking funds or longer-term savings. Cover any move-in/setup buys from your existing $3,000 so your monthly categories stay steady while you learn your true spend.
If you can find one used a Baby Jogger City Mini is a great fit for your needs - true one-hand fold, sturdy frame, bigger wheels for rough sidewalks, and often under $200 secondhand. New in your range, check out Graco NimbleLite, Contours Bitsy, or Kolcraft Cloud Plus; prioritize a 50 lb or higher weight limit and lockable front swivels, and a standing fold so it’s easier on stairs and buses. A little upkeep helps it last: tighten screws monthly, hit the hinges with a light silicone spray, and use a simple strap or gate-check bag so it stays closed and avoids dings when you fly.