'Men smile at me.'
Unless you are living in planet Mars you would be aware that simple basic interaction beween humans involves a smile. On planet Earth a basic form of acknowledging another human without having to say a word is a smile.
When you walk the 'streets' you may notice the odd human male and female glance and smile as a sign of non-hostility and kind gesture. The 'natural' response of the recipient human is to return the gesture with a simple smile.
Humour aside please keep things on normal range and perspective and use your God given common sense to judge how to respond. Smiling to a stranger and saying hello good morning or making small talk about the weather or about their dog (since your child responds to it) is a mark of respect and basic common small talk. Usually a walk in the park is the only place different cultures come together. Often a smile is the best gesture of kindness and non-hostility as cultural norms and languages are so different.
So my advise: smile back returning the gesture and walk on...
Saying that if you don't feel the need to smile then keep a natural smile while averting your gaze, or assuming to busy with your child or whatever without offending anyone or seeming over- zeleous if that is your worry.
I'm not sure what thought process your question stems from but if your looking for a religious injunction on day to day matters pertaining to women and their social role/hijab etc then it is a very contentious area. Rulings on these things are based upon traditions , customs and cultures. O suggest you use basic common sense without offending anyone or compromising your own principles.
Seek purification of the heart (I recommend Sheikh Hamza Yusuf book on this) and seek to focus on your inward reality.
Have a good opinion of people in general. This is a islamic principle of character known has 'husnuz zann'. It means thinking well of people. So if you can't tell why somoeone is smiling at you - you should think it's out of curtesy and kindness between strangers not anything sinister. If you walk out thinking every man is attracted to you and has malice in his heart your heading down a slippery slope that is neither beneficial to your spiritual growth or to those around you- as it harbours vanity, self-righteousness and misjudgement of others which you will then project negatively onto others. It can also create a state of delusion in your head where all you see around you is 'fitna fitna...haram,haram' all men are 'bad'- all women in non-hijab are bad, hijabis are good etc.... and you start polarising everything onto black and white, good and bad and becoming highly judgemental of others and over occupied with the outwardly appearance.