• From Milano Malpensa Airport: Take the S50 train line Bellinzona-Malpensa (direction: Bellinzona), and get off at Varese. The timetable of the line S50 is here: https://www.trenord.it/en/routes-and-timetables/journey/our-lines/biasca-bellinzona-lugano-varese-malpensa-cross-border-line/

• From Orio al Serio Airport (a.k.a. Milan-Bergamo Airport): If you are landing at Orio al Serio Airport, there are two options.

1) The first one is to take a shuttle bus from the airport to Rho-Milano Fiera train station (see the timetable here: http://www.orioshuttle.com/_eng/Orio-al-Serio_Fiera-Rho-Milano.cfm), and then hop on a train toward Varese (local line or line S5).

2) The second option is to reach Milano Centrale train station from Orio al Serio Airport (there are several shuttles operating this trip); then reach Milano P.ta Garibaldi train station via the subway line M3 ("yellow line"); finally take a train (local line or line S5) toward Varese. You may check the timetables of the trains from both Milano P.ta Garibaldi and Rho-Milano Fiera to Varese (beware: just «Varese», not «Varese Nord») here: https://www.trenord.it/en/

• From the Gotthardbahn: If you are travelling through the Gotthardbahn, you can get off at Lugano station and take the S50 train line Bellinzona-Malpensa (direction: Malpensa), then get off at Varese. The timetable of the line S50 is here: https://www.trenord.it/en/routes-and-timetables/journey/our-lines/biasca-bellinzona-lugano-varese-malpensa-cross-border-line/

How to reach Villa Toeplitz once you are at Varese train station: take the bus line C or line Z (the bus stops is in front of the station) and get off at S. Ambrogio stop (here: https://goo.gl/maps/hXYE8NnjHiMbic3L9). You can reach Villa Toeplitz with a few minutes walk.

The timetables of the bus lines in Varese can be found at https://www.ctpi.it/IT/LineeUrbane (but in italian...)