hello, I am currently attempting to design a siege of a large city for my current campaign with a part of 4. I’d like to include as much action as possible, but I’m not sure how to go about it. My ideas were to give them chances to sneak into the city through underground tunnels but I don’t want to railroad them into a single decision. My question is how to design multiple aspects of a siege so the players have many options to do whatever they pleass to take the city with their allied army. 

Also, any ideas on extra features of the siege would be gladly welcomed. Thank you. 

So, since your players are with the besieging army, there are two main ways to speed up a siege, with a number of possible ways of achieving them:

1) find a way in ...
1a) through the "front door" - attack gates or weak parts of the walls in an effort to get in. Ways to help: examine city defenses, force the city to use up ammo, including 'siege ammo', find a super-weapon(!).
1b) through the "back door" - find clandestine or DIY ways into the city. You've already suggested this yourself.
2) disrupt the city's supplies
2a) food - wait a really long time, and eventually someone will run out
2b) water - disrupting water will send everyone inside balls up sooner. Can include physically stopping the water source, or literally poisoning the well
2c) combat supplies - basically, disrupting the defenders' army weapons, armour, etc. e.g. you find their stash of arrows, or their best blacksmith, etc. Hard to defend if you have no swords, etc.
2d) morale - propaganda war, could involve spies insinuating themselves amongst the defending civilians, stirring the pot, complaining about how bad the siege is, making the population discontent in anyway possible, to reduce popular support for defense, perhaps form an uprising, or at least, distracting the defenders because people need to be put on street watch, so that they are less coordinated because of suspicions of political rivals or something, less able to focus entirely on defense

I think you are falling into the trap of thinking it is your job to provide the PCs with a way in.
Design reasonable defences, know the resources available to the defenders, then ask the players what they are going to attempt. Do this in advance of the actual game session, so that you can put some thought into fleshing out the defences/obstacles they will face attempting their plan. Otherwise you are likely going to put a lot of work into areas that are never needed.

The PCs may fail, but at least it was the player's plan. Or they may succeed, and the victory will be all the sweeter for knowing it was all theirs.
Failure probably means capture and imprisonment within the city - now what kind of party can't escape from a dungeon cell? Failure may be the easiest way to enter the city!

I would suggest that unless the party are very low level, getting in may well be the easy part.

Edit: Of course, once the PCs are in the city, as JCAUDM says, they will most likely be there to cause havoc - in my experience, this is what players and player characters do best. Be prepared to be surprised.
Hold on tight, try to enjoy the ride, accept that you are no longer in control.
I think you are going to have a blast. And your players even more so.

You could transfrorm abandonned siege tower into nice dungeon;) player will climb it up level by level figthing with defenders trying tu burn it down. you could also add some plot twist with undead etc

A siege, I know a siege, now there's already a lot of good advice so I'm gonna throw in something I use for a lot of my sieges, rather then regular combat I do what I call MASS PANIC COMBAT, basicly as the events unfold the initiative order is GONE in combat, letting a party member do a full turn of action having them be attacked once or twice then next person, next person, big event, other crap happening, its chaotic, but, honestly I've had some of my best moments with this system