Current prices range 200k-300k, with the average being in the middle. The lower end of that price range around the 200k will get you a pied a terre in an average building, probably in the Quartier Musiciens. It will be 30-40m2, won't have any outside space, and will need 'refreshing'. There are also cheap deals in the Old Town, but be wary as there is now a lot more buy-to-let there, renters have become more picky, and a dingy 5th floor (no lift) appt with poor communal areas is no longer considered 'quaint'. Anything under 200k and you are better off with a studio, as it's unlikely the 1-bed will be in an optimal area for rentals.
At the top end around 300k you should expect a brand-new renovated apartment in a nice building, good facade and communal areas, with a balcony or terrace. Anything over 300k must have something exceptional, like a huge terrace, otherwise you are much better off going for a two bedroom in that price range.
If I were you I would look at property around the 270-280k mark and try and secure it for around 250k. You should sacrifice size for location, a 35m2 appt in the Carre d'Or near the beach will rent more than a 55m2 appt in the Quartier Musiciens near the train station. There are currently good deals in the Fleurs area but do not go further west than Grosso. South of Debouchage is also has a few good deals but do not go north of there. And a balcony is a big plus, no matter how small it is.
Do not go outside any of the areas mentioned above, and if you see something on the 'net that looks too good to be true then it probably is. Our system holds every property for sale in Nice, and I can tell you there are good value for money properties but no real bargains. If someone tells you something is a good rental property, do not take their word for it. Call up a rental company and ask!
Now is a good time to invest but a different approach needs to be taken in this new market. Before you needed to grab any value for money property on the spot, as many owners put on their properties over-priced in the knowledge that eventually somebody would pay their asking price. From now until Autumn you can afford to be more circumspect. Put in a lower offer, and if you do not get the property immediately book the next flight for a couple of weeks later and try again.
The rental yield and mortgage questions I have answered above. I wish you the best of luck in your search.
Phillip.