Areas within 10 mins of Freo, are East Fremantle (nice upmarket nr the river and plenty of parks), North Fremantle (exclusive by river and sea, so will pay premium) White Gum Valley (expensive for location, but houses with character and very close to freo), Bicton (again by the river, older houses), melville (east of freo, further inland, but good price houses without paying the premium to live by the sea). If you have working in Fremantle, i would recommend definitely residing in the vicinity, because the commute further away can be a nightmare. All of these areas are within your budget, safe and have local shops close by.