There is a hefty fine waiting for anyone who opens up a bottle of wine, can of beer, or any alcoholic drink, in the centre of the town. So don't pick up a six-pack and take it down to Jephson Gardens to enjoy a sunny Saturday afternoon. The fine applies to simply carrying an open bottle or can, and is in the region of 100 pounds, if I remember correctly. There are signs delimiting the area where the fines are in effect, but they aren't as common as you might like. If in doubt, don't risk it.
Leamington has a crime rate that belies its gentrified exterior. Almost all the obvious in-your-face crime is packed into two nights of the week, on Friday and Saturday, and there are few people living in the town who don't know someone who has been attacked. While never having been in trouble myself, I've witnessed and been involved in a number of nasty incidents. I have witnessed mass brawls break out in some pubs, with glasses and chairs breaking on people's body parts all around me, while I stand there drinking my beer. I also remember one New Year's Eve keeping Napoleon and a Chef from kicking the crap out of my friend, who was lying in a pool of blood on the floor.
It's not all bad, and most weekends nothing happens, but if you don't know the area, it's probably best not to walk around on your own. Avoid bars around closing time, which is around 11pm-12am, and be very careful walking around Bath Place, the High Street, Clemens street, and the streets behind the Parish Church. Basically all the streets between the station and the post office are worth avoiding at night if you want to feel safe. If you are coming from some big city like Manchester or Liverpool, you will find Leamington very relaxed in comparison. However, if you are coming from abroad, and are not used to the overtly aggressive nature of drunken English youths, you may find it very disturbing.
Just be usually aware as in any large town/city, you can be mugged or attacked.
I am a local and have been, as have most of my friends and my brother at some point.
England is violent at times at night.
Anywhere south of the river is quite dodgy after dark and avoid walking anywhere alone, particularly if you are female. The train station approachs have seen a number of rapes and sexual assaults.
Be aware at ATM machines that you may be taxed so look who is around before you use one.