1) The point about emergency landing areas being external to the larger size ports is well taken. At an E class, it may well be that everywhere is essentially an emergency landing spot and there isn't really much to risk. But as you move up, more collateral damage becomes possible/likely, so you'd want to shift further away your emergency landing area. I'd say not so far away that your emergency responders can't reach, but far enough that a nice big boom won't destroy everything. Perhaps all emergency landings should be made into water (no harder than ground, absorbs heat, and could cushion and explosion).
2. Airports might want large ponds (actually, open-pit reservoirs) to provide available water for firefighting or irrigation. Also might be where their drainage goes.
3. Ship parking berths: Raised walls and a slightly raised platform are probably the best long term combo - raised walls protects from the environment (and in some cases, could have huge iris or clamshell doors or even some sort of static field repelling rain or other atmosphere) which I most specifically think of wind and wind blown particulates as part of, and the raised platform (a few feet) helps avoid drainage issues. Of course, for the largest ships, a raised platform in the open is the answer - you aren't likely putting a 50dton liner in a round berth or it'd be one freaking huge berth and big wall around it.
4. Starport buildings:
a) Well distributed emergency response will require multiple locations for at least one or two emergency vehicles. An infirmary/med center will become necessary.
b) Customs facilities will be integrated into the main terminal, but some form of impound lot for large cargo or even vessels may be necessary as well.
c) Quarantine area: An area for ships to be quarantined for a period (ideally, this would happen in space before inward clearance, but who knows?). This might just be a lockable berth or it might include its own mini hotel or cargo warehouses. This would also allow ships to be cleaned up (think of the scene in the 5th element where they use flamethrowers to clear vermin off the landing gear).
d) Repair berths, of sizes varying from 10dTons up to possibly several hundred dTons, some for short term work, others for longer term overhauls (think large quonsets or just scaffold frameworks). Also, warehouse space.
e) Fuel tankage and pumps for refined fuel, fuel for local atmosphere craft, and fuel for local ground/grav vehicles. Also probably storage of stuff like LOX and other sorts of gases or liquids needed for starships (coolants, atmospheric gases, lubricants, etc).
f) Disbursed security presence. You need to keep an eye on ships, people entering from the outside world, and even your staff.
g) Storage - parts, paperwork, computer data, yard maintenance equipment, electrical gear and powerplant parts, electronics spares (if the ILS goes down, you don't have time to call offsite), etc. Lots of buildings scattered about.
h) Inspection areas. Various ship's compliance with standards may need verified. The inspectors will need a place to work (berths could double as this) but they'll need offices and record annexes.
i) Onsite hotel/hostel, SPA office, TAS office, insurers offices, ground/grav vehicle rental offices, flight schools for atmospheric craft, perhaps schools for space vehicle crew, currency exchanges, food storage and preparation (from fast food joints to a cafeteria for the staff to fancy restuarants dealing in only offworld food), bank offices, trading factor offices (to buy and sell cargos and do brokerage stuff), veterinary and non-emergency medical services, knick nack and book stores, souvenir stores, stores selling restricted or regulated goods (licqour, drugs, weapons, armour, etc), camera/communications/computer store, tourist bureau, police installation for liason with local PDs outside extrality line, customs both from the planet and the Imperial side, etc.
j) Local defense force presence (for coordination with Imperial presence). Alternately SPA, corporate goons, IBI, Marines or Army... recruiters for various local and Imperial forces. Perhaps an embassy presence (I can see coupling embassies and starports in some places).
k) Acclimatization facilities - even with breathable atmospheres, you might have atmospheric pressure adaptions, you might need a shot or two for local allergens that need some time to take effect, you might need educated on what to do if you discover you are infected with Yallow Fever, etc. - This may take some time. This could be part of the hotel complexes or immigration or wherever.
l) Firefighting services - vehicles and men need a place to live and be worked on.
m) Mandatory Starport Bar(s)
n) Any professional guild (Astrogator's Guild, etc) offices.
o) Journalist offices (TNS, local news looking to break any incoming stories from the ships arriving, etc)
p) Indoor storage for atmospheric craft. Parking areas for same. Repair areas for same. Parking areas for ground or grav vehicles that are picking people up, dropping people off, or doing business with the port or its various ancillary businesses.
q) Psionics Institute (I'm kidding - just seeing if you were still reading)
r) Silos, gun emplacements, etc - Planetary and Starport specific defense against threats in the atmosphere or space (you have your ground-pounders to stop ground threats along with some perimeter defenses).
Note their should be a tower somewhere once you get a bit further along. It lets you mount your search radars higher up (good to avoid irradiating people with powerful emitters!) and it also lets your controllers get a visual eyes-on of what is happening on landing pads, runways, and so on. Sometimes planes/ships aren't responding, but if you can get eyes-on, they you can tell the other nearby craft a bit about what to watch for. You could also respond by dispatching police or emergency response as required. So a tower serves valid purposes even at higher TL.
All of these bits will be present or not depending on the TL, political, environmental, medical, legal, or financial situation (add diplomatic too). They will also evolve over time from smaller flat-pad only ports through your swirling multi-nodal metropoli of chaos.... like your large modern airport on steroids.
