Lyon is a lovely city to spend a few days in. It is very easy to get around in the city. Everything is pretty much walkable. The Fourvière hill and church are reachable by funicular and the Croix-Rousse hill by metro. To get to the modern confluence area, there is the vaporetto boat and the tramline. You'll find Lyon a very easy city. People are friendly and ready to help. Public transport is very easy. There are nice city bikes to rent (almost for free) and there is enough to do to fill a week of site seeing.
Public transport is (relatively) well organised and cheap.
The metro or subway system in Lyon is pretty straightforward. There are four metro lines and two funiculars. A ticket costs a bit less than two euros and is valid on the busses and trams as well. If you buy more than 10 tickets, the price drops. You can also buy daily tickets. Check the website of TCL (the operator of public transport in Lyon) for more information. You find ticket vending machines in all stations as well as maps.
Busses and trams in Lyon are part of the metro system. With one ticket, you can change from a bus to a metro and vice versa. There are some nice and modern trolley busses in Lyon that take you anywhere in the city. The tram lines are also very efficient. Modern trams take you to Confluence, the train station and many other parts in the city.
Lyon has an awesome system of city bikes. For less than 2 euro you can get a daily ticket and use the bikes for half an hour at a time. A yearly pass just costs 25 euros. All throughout Lyon, you find docking station. There is even a smartphone app that shows you where they are and if bikes are available.
There are taxi stops all throughout the city. You can also call taxis, or have someone (from the restaurant or hotel) call a taxi for you. Uber works around the city. There is also a smartphone app and website where you can order taxis in Lyon.
Lyon is connected to the Saint-Exupery Airport with a tram link, the Rhônexpress. It's a very convenient way to get to the city, but relatively expensive (compared to other European cities). The tram stops at metro stop Vaulx-en-Velin - La Soie, from where you can take the subway to Bellecour. If you stay in the tram, it takes you to Part-Dieu, the main train station.
If you are staying around the city center, everything is pretty much in walking distance. Lyon is a very easy city to walk around. The main areas of Vieux Lyon and Presqu'Île are flat and easy to get around. Most of the highlights of Lyon are located pretty close to each other. Some, like the hidden passageways of Vieux Lyon, can only be explored on foot.
Lyon is called the culinary capital of France. When you are here, make sure to enjoy some of the great food. Here is some practical info about eating in Lyon
During the week, most French restaurants offer a cheap day plate, the plat du jour. It's a great way to eat out for a small price. Many of Lyon's nice restaurants have an inexpensive day plate. Remember, a bottle of tap water should always be provided for free. If not, just ask for a carafe d'eau.
The Bouchon are the traditional restaurants of Lyon. They serve hearty meals in an informal setting. Try some of the classic dishes, such as the quenelle de brochet, tripe a la lyonnaise or andouillete. Better not to look up what these dishes are made from. If you are a vegetarian, better to skip the bouchon.
In France, by law, service is always included in the price. However, it is becoming more customary to leave a little tip. You can round up the price of your meal, or leave about 5%. In bars, nobody really tips, but the waiter or barman will surely appreciate the gesture. At a coffee place, it's not customary at all to leave a tip, but you can leave a little change.
You can obviously get amazing wines in Lyon. Go to a wine store and let the people help you. Tell them your budget, and they will surely come up with an amazing wine. It's also lovely to go to a wine bar. For 5 euros you can get a great glass of wine. Again, ask the barman for some of his favorites and you'll get something special most of the time. Local wines are the Côte du Rhône and the Beaujolais.
You can drink the water from the tap without problems in Lyon. In a restaurant or eatery, they are supposed to serve you free water if you ask for it. This is a law in France. Ask for a carafe d'eau and they will bring you a bottle of tap water. This can save you quite a bit of money.
To explore Lyons food culture more extensively, go to the Michelin website. Here, you find all the starred restaurants and also the Bib Gourmand, the restaurants with the best quality/price ratio.