First, we can't balance your budget for you. You'll have to sanity check your numbers yourself. One piece of advice : your city probably spends less on bureaucracy and services than you think. Cities did not really get that organized until industrialization apart from special cases such as Rome which was at its height just too big to do without extra administration.
But that reduced administration does give some pointers on the taxes. You need taxes that are fairly simple to administer and hard to avoid.
Generally you would be taxing the means of production and generating income, not the production and income themselves. Much less bookkeeping means much less opportunity for cooking the books.
Agricultural land is a favorite as it is fairly difficult to hide from tax collectors or to move to a city with lower taxes. Tax would be based on area and area ;). How large is the property and where is it located?
Buildable properties within cities would also be taxed similarly.
Specialized tools such as anvils, forges, kilns, or ploughs can also be taxed with preference on those too large to hide. Making noise or clouds of smoke when used is also good.
Means of transport such as carriages, carts or ships can be taxed with tax tokens attached to them and occasionally checked. In many countries cars are taxed similarly today.
Animals of economic significance can be taxed. Preferably large working animals such as horses and oxen. Cows and sheep can be also taxed. With horses and sheep the kind might make a difference on the tax. Such forms of wool have much higher value than others and horses bred for different purposes are quite different.
Slaves might be considered means of production and taxed based on their skills.
These give you a right to do something that the authorities can reasonably stop unauthorized people from doing. An easy example from your question is entering the city.
These are generally called fees rather than taxes. Examples are entering the city. Bringing a cart or carriage into the city. Bringing a carriage into roads controlled by the city. Docking a ship in the harbour.
Paying for the right to reside within the controlled area is also possible. The rights and prices can have levels. A slave might be cheaper than a free man. Unless they are considered as a means of production in which case they might be more expensive. Voting rights might require a higher tax. Right to own certain property or operate a business might require a formal license and a higher fee, generally organized and enforced thru a guild system.
Instead of collecting taxes it is often simpler to require citizens to provide service for free (possibly with financial support provided by state for those needing it). Modern way of doing this is by tax deductions, ie. you do something the state considers valuable and can deduct the cost from your taxes but this requires too much bookkeeping for pseudo-medieval city, so flat tax exemptions or granted monopolies would probably be used instead. There is a plethora of possible privileges that can be granted.
Common examples would be military service with equipment bought by the citizen, days of labour per year for city walls, roads, irrigation or other infrastructure. Administrative help is also possible with guilds for example helping with tax collection and law enforcement in exchange for privileges.