No need to wonder any longer.
Education takes a massive amount and is the most expensive of all council services, with social care the next biggest spend. Those 2 alone account for approx 2/3 of all local authority spending.
Some of it will be the police and fire and rescue precepts, and doesn't go to the councils at all.
Then there are all the smaller statutory services: things like libraries, trading standards, environmental health, planning, building control and weird odds and sods like the registration and coroner's services.
Highways and transport spending (including spending on public transport) where I live was less than 5% of the total spend of both councils last time I looked at the budget breakdown. As almost all the roads in this county (and the neighbouring one, now that I think about it) are "county roads" and not managed by the Highways Agency, the cost of maintaining them has to come out of the council's budget. In areas with a lot of motorways and major trunk routes, the busiest roads aren't the council's responsibility.
There is limited scope for making savings from the education budget, because most of it is delegated to schools under a set formula, and savings in social care are hard to make because it is essentially needs-driven. Every time cuts have to be made because the central government grant isn't keeping pace with inflation, the axe falls on the smaller services, like libraries and highways.
Disclaimer: breakdowns may be different in London boroughs/met authorities/city councils where there's only one tier of local government, but I wouldn't think there's a massive variation.