Only the first sentence is correct. When you talk about a situation which you would like to be different, you need to use 'wish' + the past tense. I wish I lived in California. I wish I had a big car. I were rich. (note that you use the 'were' form for all persons). The second sentence is wrong - you don't use 'would' to talk about wishes about yourself. You can use 'could' to talk about something you 'can't' do but would like to, for example 'I wish I could speak English fluently, or 'I wish I could lose some weight' - but not 'would'.

The first is a state, the second is an action. "I wish I was a non-smoker." "I wish I would stop smoking."