Solentiname Islands is in Nicaragua on the Southeastern corner of Lago Nicaragua.
The Solentiname Archipel is situated in the south of the Nicaragua Lake near San Carlos. The islands are really remote - don't expect things like grocery stores etc.
There's one pretty expensive hotel, plus a hospedaje, where you can stay for around US$3-5 or so per night including meals.
The only way onto the islands are via boat. Private boats can be chartered for around $100 per day. Otherwise collective boats leave from a pier in San Carlos near the current construction along the seawall. The schedule is San Carlos to Solentiname Tuesday and Friday 1pm for C$80 and returning the same days at 4:30am for the same price.