Solentiname Islands is in Nicaragua on the Southeastern corner of Lago Nicaragua.
The Solentiname Archipel is situated near San Carlos, Nicaragua. 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 incl. 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.