My gf has a sig p238 she has for SD. I don't know how you feel about single Action only pistols but she uses hers very well(possibly because most of what I've had are 1911's and she's shot them and likes the way they shoot/handle)
Anyways they shoot great, are very accurate and easy to be accurate with for a pocket pistol. And if your not into the .380 thing, they make a slightly larger version in 9mm(p938)
The biggest con of them is the cost. I know I wasn't happy spending that kinda coin on a .380 but it's what she is comfortable and good with. I carried a p238 as a back up for awhile. They are reliable and I've never had an issue with them.
LCP's are excellent for the price but the trigger is long and took me a lot of practice to be proficient with it.
Good luck with your choice, No matter what you get practice is key. Shoot it as often as you can.