Anchoring is one way to maintain position.
We should distinguish two different types of systems: permanent Mooring and retractable anchoring. Ships come equipped with a retractable anchoring system, but the accuracy of such a system is limited, as an anchor may drag across the ocean floor.
Permanent anchors/mooring systems are used for offshore platforms. They provide greater reliability than a typical retractable system. One means of setting a permanent anchor is by means of suction anchors.
The cost of anchoring is a function of depth, as the cables (see: Catenary represent a significant part of the cost. And of course, the cost is a function of maximum force, which strongly correlates with total displacement.
Some data is available in [here], p3.
The setting is 6000ft water depth in the mexican gulf; the anchors are capable of withstanding hurricane force.
1M$ for a 1600st structure, and 4M$ for a 5500st structure.
These are material costs; installation costs are unclear, as they are lumped into another category. Including worst-case installation estimates, mooring costs are about 1/3 of total costs.
Assuming 50 people on a 5500st structure, the cost merely of getting a fixed location is large compared to what you would pay for land prices.
See a video on anchoring: How To Anchor a Mega-Ship - Anchoring & Equipment Explained! - Life at Sea JeffHK on Youtube