Lunch option - I would recommend Feel Myanmar. Great way to experience a good spread of authentic Burmese food. Popular with locals and expats, its similar to a buffet where you can go and point & choose various dishes. Talk to the wait staff and have one of them make some recommendations. Its located on Pyi Htaung Su Yeikthar Road, but any driver will know Feel Myanmar.

Else if you're downtown, try Nilar Biryani on Anawrahta Street, couple of blocks from Traders Hotel. Popular with local lunch crowd, cheap and will fill you up!

A walk around Kandawgyi Lake offers various food/restaurant/cafe options and a chance to mix with the locals - Royal Garden does a popular dim sum there too with a view over the lake.

A walk around the heritage buildings of downtown Yangon is worthwhile and another good chance to see the city centre. Start on Strand Road at The Strand Hotel, and wind your way back north towards the Sule Pagoda.

Agreed on the recommendations above to do a sunset visit to Shwedagon.

If you do want to pay for a tour guide/driver and have a car for the day - contact Dr Thant or Miss Kyaw at Myanmar2Go. Highly recommended and worth the money to make the most of a day trip.