Unfortunately, it's hard to find a way to allocate land without using the market. Yes it's unfair that rich people have to pay more to live where they want than poor people who are happy living near other poor people, but how else can you allocate land that gives the useful land to the people who'll get the most value from it? Central planning doesn't get it right, a lottery would mean people can't group themselves together so they would lose that important value (eg programmers in Silicon Valley).

Land value tax would take money from people who don't need those community services and give it to different people who happen to live nearby. That's not really fair. It's still a kind of rent seeking that also happens to give the rent to charity but not back to the original payers in proportion to what they paid. But it does sound more reasonable than the luck of the draw that property owners get.