I'm gonna make a few assumptions: One is that this is just a neighborhood in my hypohetical ideal world (or rather, near-ideal). Second: we're talking about high qualiy versions of these places, and not the "just barely good enough to not go under" versions that abound. Last: "should" means "necessity" and not "luxury."
Groceries are a no-brainer.
Parks — hell yes. In fact, I'd prefer if everyone had access to all kinds of nature within "walking" (walking + public transportation) distance: parks, woods, botanical gardens, community gardens, wildlife reserves.
Pharmacies should be obsoleted: drugs should be devriminalized and un-gatekept. People should have the freedom to put whatever stupid, life-altering substance they want to into their body (with caveats like informed consent and heavily recommended medical professional supervision). Distributors could be home-delivery through the post and the over-the-counter section in your local grocery store.
Bus stops... Yes for some neighborhoods, but ideally more trains or trams, especially in suburbs.
Post offices are dying out. Letters and spam are the kinds of things people should have access to in their immediate neighborhood, but are becoming obsolete thanks to the internet (which should be a public utility instead of run for profit). I'm about 50/50 on whether there should still be home-delivery for everyone and all packages, or if there should be local holding centers for most (although, once again, any delivery network should be considered a public service instead of a few companies monopolizing the role), and at-home delivery for the most important packages/incapacitated people.
Banks are a no. Credit union, yes. Or maybe no and just let money become the digital currency it's slowly been turning intobfor the past 40 years. Ideally, society (and by extension this ideal neighborhood) would function without capital.
Gas stations: hell no. Convenience stores yes (or just all-in-one grocery stores). Maybe EV charging stations... Maybe.
Having a barber is way more convenient than people give it credit, and it doesn't benefit from centralization. At the very least, everyone should have a neighbor who cuts hair well.
Bonus round: things that should be within a 30-minute commute (by transit)—mall, movie theater, hospital, elementary school, day care, university, restaurants, bars.
No to stadiums, but yes to sports fields in the parks.
Things not on the list that should be: museums, clinics, dentists, optometrists, psychiatrists, veterinarians, pools, gyms, community centers/general use indoor halls, fire stations, makers spaces... probably others that I'm forgetting.
Sorry that this 15 minute walk is turning into a jog.