Here are details of live-to-cinema broadcasts of plays, operas and ballet coming up in the next couple of months. These are not being shown in all cinemas so you will need to check listings for cinemas near you if you are interested. All these are AFAIK live broadcasts apart from the Glyndebourne showing of Falstaff on 17 June which is from a recording in 2009, and the next day repeats of Globe Theatre performances.
3 June - Globe on Screen: Henry V (repeated 4 June)
4 June - Glyndebourne: Ariadne auf Naxos
6 June - Mariinsky Theatre: Swan Lake
13 June - NT Live: The Audience
17 June - Glyndebourne: Falstaff
24 June - Royal Opera House: Gloriana
1 July - Globe on Screen: Twelfth Night (repeated 2 July)
8 July - Glyndebourne: Le Nozze di Figaro
20 July - NT Live: Macbeth
25 July - Glyndebourne: Hippolyte et Aricie
I think also on 25 July there is a live cinecast from the Bayreuth Festival of Der Fliegende Holländer (at least, it is advertised in the Malvern Theatres programme).
3 June - Globe on Screen: Henry V (repeated 4 June)
4 June - Glyndebourne: Ariadne auf Naxos
6 June - Mariinsky Theatre: Swan Lake
13 June - NT Live: The Audience
17 June - Glyndebourne: Falstaff
24 June - Royal Opera House: Gloriana
1 July - Globe on Screen: Twelfth Night (repeated 2 July)
8 July - Glyndebourne: Le Nozze di Figaro
20 July - NT Live: Macbeth
25 July - Glyndebourne: Hippolyte et Aricie
I think also on 25 July there is a live cinecast from the Bayreuth Festival of Der Fliegende Holländer (at least, it is advertised in the Malvern Theatres programme).