Sure, but also TAX the property based on it's /potential/ value.
A land owner close to where the city is now shouldn't be able to squat on that land at the cost of the opportunity it can provide to the neighborhood(s) around it.
You can capture this by assessing the value of the land (regardless of what's build on top). Downtown detached houses are more valuable because the land they sit on is near other stuff, and people want to be near stuff. They are not valuable because the owner installed a new marble counter-top.
Should we also TAX vacant or idle storefronts that seem to have zero foot traffic any given hour of any given day?
(SF seems to have dozens of those every city block. One wonders if those are some kind of fronts for illicit activities. They seem to never change ownership even with skyrocketing rents for office space nearby.)
Should a street level business that serves a large number of residents, get TAX BREAKS? Like a grocery store that vends fresh produce as opposed to a boutique book store that specializes in first editions?
Should they also get favorable lease terms, mandated by the city?
Should businesses that, by nature, serve out of town-ers be forced to move to designated neighborhoods?
Should empty storefronts be forced to take up tenants who could serve the needs of the residents?
Is TAXING even the solution to any of these problems?
Yes you should tax empty land, just by taxing all land. The land owner always has the option to sell the unused land. It encourages property use, and the tax rate actually decreases the more built up the property is. This is not rocket science. Land taxes are well established in economics literature.
It's probably very complicated, but I would answer yes to many of these questions. I think it would be worthwhile investigating a model where every home has a mini-grocery with affordable prices within 2 blocks of every home in these neighborhoods - and to achieve affordable prices, there may have to be some tax breaks involved, with some accompanying price limits on "staples" (bread, milk, etc). Difficult, yes; impossible, no; worth it, I think so.
Come to cities in Germany. Everwhere I lived the next supermarket was less than fifteen minutes walking away. Price and density are inveresly proportional.
"Every two blocks" is a bit much for anything but the densest of high-density areas. Even the convenience stores aren't clustered that closely in my city's downtown.
Subsidize what you want and tax what you don't is 101 level economics. Distort the market to match what neighborhood wants. There are other approaches, but macro is pretty well understood.
To a large extent this already happens, and is one of the major complaints about gentrification. The rising value of the land & property causes rising rents, which can become a hardship on the lower-income people who were living there before the place became trendy/valuable.
Not to say it shouldn't be done, but there are definitely two edges to that sword.
A land owner close to where the city is now shouldn't be able to squat on that land at the cost of the opportunity it can provide to the neighborhood(s) around it.