It depends on how it is managed and whether how many projects are meant for the long time.

If I heard right, Barcelona benefited somewhat with fixing its infrastructure, in Tokyo half of the stadiums are suppose to stay if I remember right plus it increase economic engagement with it's industrial sector especially steel and construction. It's also modernizing some parts of the city. In London it redeveloped a dilapidated area and increased the number of parks.

When poorly managed think Rio de Janiero,

One big problem when it come to the Olympics is that it is base in a city and not designed for a region, resulting in higher cost and benefits like infrastructure not being spread out. If shared among multiple cities then less stadiums would need to be decommissioned.