There is a number of options that have been already touched upon. If there is a demand for a particular service, people will find a way to provide it.
Keep in mind that medieval cities often didn't deliver the services you mention in the first place. Especially water supply was a sore point even after it was recognized how important it is - and that took a long time!
Some of the items you've brought up (notably pavements) can and will be provided by the guilds themselves in their places of interest. Nobody wants to have a beautiful guildhouse surrounded by a swamp; similarly, places of trade need roads of at least some quality. People built roads without a central authority all throughout history as they do now.
Guilds can assume responsibility for specific parts of the city, with the rest being left to whoever is inclined to maintain them; probably whoever is living there or has to pass through.
The potential problem here is a hodgepodge of roads and pavings of highly varying quality and nature (although any medieval fantasy city is likely to have that anyway). Streets and roads can feature tolls, possibly applying only for some loads and travelers (e.g. wagons only) and can have weird rules for usage. Make sure to emphasize this during chases - in some places the heroes slip on the slick stones, in others they have to slow down to throw in a copper to pass. In yet others they can cross but must stay silent etc.
True Roman bread for true Romans
Guilds (hopefully) don't just focus on hoarding money, they also take care of their members and help out the wider community. They don't have to be altruistic at all - it makes perfect business sense to be seen doing good, especially if the guild members also profit.
The flipside of this approach is that much like today, the highly visible and popular projects will have priority over the necessary and boring.
The powerful guilds are also likely to try going at major projects alone, even if they can't really finish them. The lure of great income and/or prestige has brought many organizations down - and many will be eager to help them go down.
As pointed out by others, magic can make many tasks easier, especially in construction. You could also have priests cast repeated purifying spells on the water sources to supply the masses with clean water. (If you don't want to go outside of the guild structure, you can make those priests/magic users another type of guild, that everybody contributes to if they want water... just a thought.)
The downside of this is giving magic users a lot more influence and at the same time annoyance because they serve as common laborers. What could possibly go wrong?
A public fund could gather the money and resources needed for a vital piece of infrastructure. The project will be managed by a known group of people and may be well-defined in advance.
This approach can run into trouble when costs inevitably overshoot the budget, or someone refuses to pay up their IOU, do the promised work, etc. Public opinion can change and leave the project half-financed.
A number of guilds has agreed to cooperate on a long-term project. Each of them will work on it and finance it for a month or a number of months, taking turns.
There is of course the risk of some contributors dragging their feet, doing sub-par work or even sabotaging others to make their work shine more.