Seeking neighborhood & apartment hunting advice

Hi r/movingtonyc! I’m (29F) moving from San Francisco in the next few weeks and would love some input on three things.

1. Neighborhood recommendations

My vibe is pretty low-key — I like good restaurants nearby and walkable parks or outdoor spaces. I still want to feel like I’m living in a city but not have it be too loud or crowded. Open to Brooklyn/Williamsburg but don't want to be too far out. I'll be commuting to SoHo for work 3 days/week. Budget for rent is ~$3,500 for a studio or 1BR. What neighborhoods would you recommend?

2. Apartment hunting and timing

I'm planning to arrive this summer. Trying to decide between:

1. Locking in a lease now/on arrival (summer), knowing summer is peak season and prices are higher

2. Finding a short-term furnished rental for 2–3 months and waiting to sign a real lease in the fall when the market cools

For the type of place I'm looking for are the fall savings worth the hassle of moving twice? Relatedly, what are the best resources for finding apartments beyond StreetEasy?

3. Shipping stuff cross-country

I know this is slightly off-topic, but since this is a moving sub — I'm moving with 2 large suitcases and about 7 medium sized boxes under 15 lbs each. Has anyone shipped boxes cross-country rather than using a full moving company? Curious what services people found actually cost-effective for a small load like this.

Thanks in advance — this sub has been helpful just to read through while planning.