You can't really know what to look for in a neighbourhood until you know exactly what you want. Make a list, take your time. Write down the things that really matter to you. Decide priorities. Order your list from most to least important. Moving in with your partner? Have them do the same, and see where your priorities line up and where you diverge. Now that you know what you want, it's time to go get it.
Search the streets.
Don't underestimate the importance of this step. You really can't know a neighbourhood until you've walked its streets at several different times of day. Get a feel for the level of traffic and noise, decide if you're okay with it. See how the streets feel. Are they lit enough at night? Would it be nice to go for a run through your neighbourhood? Make sure you visit each of your candidate neighbourhoods.
Search the stats.
While you hunt at street level, make sure you take your research to a bird's-eye view at the same time. You would be amazed at the kinds of things you can learn about a neighbourhood just from its census data. How old are people there? How many kids are in the neighbourhood? How many people are home owners? How much are the average monthly costs to live there? What languages are spoken in the neighbourhood? Combine your research with your street-level hunting and you'll soon find yourself walking through the perfect neighbourhood for you and your family.