If it's 125cc then it's not a moped anyway. I think you mean Scooter. A moped is under 50cc and restricted to 30mph. Everything bigger is a motorcycle. A scooter is a style of motorcycle.
That said, don't bypass scooters so quickly. I have 30 years and over 450,000 miles on bikes and, until last year when my work moved out of London, I had a big bike for riding weekends and holidays and a 125cc Piagio scooter for commuting. Compared to bikes, the 'twist and go' scooters get better mileage, they are often faster from the lights ( important in a city ) and you don't knacker your left hand pulling the clutch in all the time. On top of that, you don't have to maintain them as much. With the better mileage and lower maintenance you should save a fair bit a year. Commuting 14 miles on a 125 scooter instead of my 650 saved me around �500 a year even with the extra insurance and tax. Even compared to a 'proper' 125 you should still save a few hundred. They are also available in a huge range of styles so you should find at least one you don't mind.
If you insist on a cruiser style, remember that they are a lot harder to handle in town. You want a short tall bike for the city and not a low long one.