Day 0 - Friday 19
(This doesn't count as it's not a holiday)
There are a number of options for an early start:
a) Load your family into a car or use public transportation and follow the smell of cheese, beer, and other welcoming odors.
b) Postpone a) until Saturday morning and lose yourself to dance, watching the "Tanzwut" (Dance Mania) performance, part of the Time to Dance festival, which continues until June 20.
c) Enjoy vocal performances at the Great Hall of the National Opera. You are in luck, because information at the ticket service seems to indicate that more people have chosen a).
Day 1 - Saturday 20
Those who are run down by allergies or are sworn city-dwellers will want to learn the sleekest moves Latvian folk dance has to offer at the anniversary concert of the folk dance ensemble "Teiksmiņa" at Kipsala hall. Or for the more internationally minded tourist, there's Prokofiev and Beethoven as performed in Jurmala by Latvia's finest musicians.
Day 2 - Sunday 21
Combine a countryside getaway with a visit to one of Latvia's finest concert halls. The ballet concert 'The Originals' in the Gors concert hall in Rezekne features renowned performers both from Latvia and Lithuania.
Day 3 - Monday 22
More folk dance? Why, here you are. The folk dance ensemble "Līgo" (basically another term for Midsummer) has an anniversary concert in Riga.
Day 4 - Tuesday 23
Public transportation is free on the 23rd and the 24th!
As it's free thanks to the Riga Municipality, every bus and trolley and tram should get you to the municipal celebration on the bank of Daugava river. Beer, cheese, and bonfires, all that and more within the heart of the capital!
Day 5 - Wednesday 24
Since everyone is 'under the weather' on the 24th, you might as well watch some Latvian TV. The whole holidays are filled with gems of Latvian culture.
Along with the legendary 'Limuzins janu nakts krasa' (A limousine in the color of a midsummer night) showing on the 21st, you can see Midsummer concerts and theater productions every Latvian knows on Latvia's National Television throughout the holidays. The TV guide is available here, though you might want to brush up your Latvian beforehand.