There are many, many post offices in my area in 4 different states that are all in Zone 1 for me. Some use the same sorting location, some do not. I have never had a problem with Priority Mail showing up as an option. In fact, it has to show up if the item being mailed weighs more than 12 ounces. Make sure that you input a weight of 1 lb 2 ounces to be sure that you trigger priority mail. I mail from PA to DE, 12 miles away. It takes 2 days by Priority Mail because two different sorting center are involved. One day to get to the PA sorting center. Overnight to the DE sorting center, the next day to get from the DE sorting center to the local office, and then delivery on Day 2. Same if I mail 90 miles away to NJ, or 1000 miles away in Zone 4. Two calendar days.
Shopping Southeast Pennsylvania, Delaware above the canal, and South Jersey since 2008