First off, Len, I would say it depends on the size of the hospital (and therefore, hopefully, the number of biomed techs involved). As a "Rule of Thumb" I would suggest that it is probably not worth considering for less than a 100-bed hospital.
In one of my "previous lives" I was involved with Hospital Design Teams (aka
keeping architects restrained within the bounds of reality), and - based on my own experiences of supporting equipment in-house at a number of 350-plus and 500-bedded hospitals - I always used to include a sub-workshop within the "clean zone" of the main theatres. Upon visiting one such site a year or so after completion, I was even thanked by the biomeds for my foresight (...a very rare event)!
My insistence was based upon the success I had some years earlier in keeping one of my guys in theatre greens (other colours may be, and indeed are, available). This was Good News as it meant that, not only was biomed assistance readily to hand in case of any "emergencies" (flapping) that occurred up in theatres (thereby saving me the pain of getting changed into theatre garb
a couple of times each day myself), but servicing of all the theatre kit was done quietly (usually during the evenings) without having to drag it through the hospital and down to the basement where our main workshop was hidden away.
So I would say "yes" (and agree with Dave) - theatres are the prime candidate for a sub-workshop - plus a permanently assigned biomed tech (who could be on a roster system if no willing volunteer* can be found).
By the way, in well-designed hospitals the clean side of CSSD (TSSU, Sterilization ... whatever) should be adjacent to the main theatres - so "our guy" can also take take of kit in there as well.
In a large hospital, ICU may
be another candidate - but probably not always manned; but there is often a "spare side room" available in such locations, anyway (such as where the blood-gas analyzer used to sit - a place where I must have spent hundreds of happy hours over the years). I have also seen "small workshops" tucked away (hidden?) in large Maternity Units and (or) Neonatal Units; but these were really small store rooms (not much larger than cupboards) where parts and a couple of special items of test kit were kept.
Off-site Mental Health Units (of the "secure" type) may be yet another possibility - for reasons of "security" mainly - of both tools and test equipment, as well as biomed staf. Dialysis units - especially if detached from the main hospital - could also be considered for a sub-workshop. Anywhere off-site really, where a biomed might have to spend relatively long periods on a regular basis - especially if special clothing is involved. Plus, of course, at any off-site - or remote - Clinic(s) or Outstation(s) that you may be responsible for; a small workshop (store room, broom cupboard) under your control (lock and key) can save you having to cart so much kit (tools, test equipment, spares, manuals) about in your vehicle. It can also serve as a place of respite ("safe space" in current UK terminology) where you can "take a breather" (and maybe even a cup of tea).
Another one I have used with success (at a large hospital) was attached to the clinical laboratory complex. It was a good place to store the special parts needed there, and also provided an "office" where visiting servicing engineers could "report" and base themselves (kettle essential) rather than having to go off and find the main biomed workshop. Luckily that site was large enough (and I had enough good blokes) to post a tech there permanently; he was yet another lucky guy, working on interesting kit. And don't forget that "Lab" is generally the largest department in the hospital (kit-wise, at least).
Finally, if you are a service contractor - and I'm assuming that you're not, Len - rather than in-house staff, be sure to include a clause when negotiating your contract that you shall have (sole) access to a suitable room somewhere handy at each location you are to be responsible for. This might seem seem like a small point (especially at a time when you're keen to get things agreed regardless), but you'll be glad later that you did (based on my own experiences, not all of which were good). But there again, as a contractor, you would also be well aware that duplicate test kit and what-have-you costs money! However, in [a country in West Africa] we justified such expenses by weighing them against the (very real) possibility of having our shiny kit "lifted" when on the road.
Lastly, if you are involved in a New Hospital Project that you shall also have to maintain after it is commissioned - make sure you get hold of a master key (one that fits every door in the building(s)). Then you can "claim" any spare room that takes your fancy once the hospital opens!
* It was a job that I used to relish, myself. If nothing else it gets you away from the "hospital politics" can can often develop in (main) biomed workshops.