I use BubbleUPnP for that:
- works smoothly
- can stream from your device to your TV (can even act as "control point", i.e. you don't need to navigate from your TV – just select it in BubbleUPnP and tell it to "play it there")
- can also act as client (to play media from other UPnP/DLNA services on your device)
- full (payed) version (license to obtain separately) enables Internet streaming – which you don't want. So perfect: free version is available, and doesn't really offer that :)
- support for smartphones and tablets alike (below screenshots are the smartphone GUI; see the linked Google Play page for tablet screenshots).

BubbleUPnP as client (left) and server/controlpoint (source: Google Play; click images for larger variants)
For alternatives, I might point you to my listing of UPnP/DLNA apps. I've not tried them all, as I'm pretty satisfied with BubbleUPnP as an all-in-one solution (server, client, and control point) – but you have the options :)