Hi naufilgazdar -
Glad we could get you started. Thanks for your dates.
You are wise not to push to see too many different places in a short time, because travel may be be a bit more effort with a small child. There is lot to do and see in and near Luzern, so you can pace yourselves and stay near your hotel or residence, but still see a lot. It could help to answer your question about activities if we know the age of your child.
The activities that you mention can easily be fitted into the time you have.
I've not been over to Switzerland since last winter to give a first hand report, but I note that Arno estimated in another thread that trails below about 1500 meters in altitude are free of snow now, and, as mid-May approaches, they may be open a few hundred meters higher. Although you quite likely will not be hiking, that gives some idea about snow amounts on mountains nearby Luzern.
A couple of webcams may help:
As you can see, there is plenty of snow left even on the Rigi at the top (Rigi Kulm) at 1800 meters, and at some of the intermediate levels , such as Rigi Staffel at 1600 meters. Lower altitudes are free of snow.
You have not specified the age of your infant.....perhaps he or she would like to play in the snow a bit?
I am aware that high altitude travel is not recommended for very young children, but I don't know if it is an issue for you. It might be worth a check with your child's doctor.
This map from SwissTopo will show you some of the altitudes at and near Titlis (as well as other locations if you scan around the map):
map.geo.admin.ch/?topic=swisstopo&lang=d e&bgLayer=ch.swisstopo .pixelkarte-farbe&X=183040.00&Y=67 5180.00&zoom=5&layers= ch.swisstopo.swissimag e-product&layers_visibil ity=false
The schedules are seasonal. Scan down the page to get the right season:
This will help you visualize the locations named in the timetable:
map.geo.admin.ch/?topic=swisstopo&lang=d e&bgLayer=ch.swisstopo .pixelkarte-farbe&X=207950.00&Y=67 9400.00&zoom=4&layers= ch.swisstopo.swissimag e-product&layers_visibil ity=false
<<"I'll be reaching Zurich on 12th May after midday, which means not much can be done on that date. ">>
That of course will depend on how tired you are from your journey, and possibly the effects of jet lag, if any.
However, you will be pleasantly surprised at the speed and efficiency of travel in Switzerland.
Under normal circumstances, you can be at the airport train station in less than half an hour after you leave your plane, even with passport control, getting a lot of luggage, getting across the street to the train station, and .getting train tickets ( easier if you have a Swiss Travel Pass...no tickets needed...).
Luggage carts are free, and can ride the escalators even when loaded. Or , there are elevators.
The train trip to Luzern takes about an hour. There are two trains per hour from the airport.
The ones at xx47 go without changes and take 1 hr and 2 minutes. The ones at xx18 take an hour and 7 minutes and require a change at Zürich main station. See attached screen capture:
The 8 minutes allow for the change is not difficult if you have light luggage, and follow the signs to "tracks 3-18" which is the main station area where the trains leave for Luzern. However, it can be a bit tight with lots of luggage, even with a luggage cart, if you come in at a lower level and have to work your way upwards. If you miss, just catch the next train.
At the main station, luggage carts are available, and they can ride the escalators (or elevators) but you need a 2 CHF coin or maybe a 1 or 2 euro coin to disconnect the cart from one of the many convenient storage queues. The coin is returned when you attach the cart to another queue near your train.
Once you get to Luzern, you will have time to walk around the old town or along the lakeside, I'm sure.
I've attached a few images taken on various trips to the region