Hi Sean
Firstly, to your last questions, yes, there is a chance of the aurora, one of the best displays I've ever seen was in mid-April one year. And April is too early for flowers.
Going beyond Reykjavík is a good idea, the further you go, the fewer people you will see.
Areas you could base yourself (by no means an exhaustive list):
A) Snæfellsnes peninsula in a village like Grundarfjörður, which enjoys a very spectacular setting, has whalewatching (Láki Tours), and is just generally a very pleasant area of mountains, dramatic coastlines and very wild beaches. There are bird cliffs at the end of the peninsula holding all Iceland’s breeding auks and there will be some birds present but their presence there so early in the season changes from day to day depending on the weather – they sometimes sit up in the cliffs in nice calm weather and then disappear completely in bad weather. Plenty of winter birds around still, Harlequins guaranteed (famous last words), King Eider well possible. 2-3 hours’ drive from Reykjavík.
B) Húsavík - the whalewatching capital of Iceland (although things down really start hotting up until the later in the spring. Great views over the bay to the mountains. Close to Mývatn and other natural wonders such as the canyon at Ásbyrgi and the waterfall Dettifoss (although this is subject to the road conditions a lot). Harlequins and Barrow’s Goldeneye a certainty (at Mývatn) and Gyr Falcon likely. Not much happening on the spring migration front at this time. 5-6 hours’ drive from Reykjavík.
C) Vík í Mýrdal – Iceland’s most southerly village. A bit of a one horse town (in common with most Icelandic villages to be fair) but I have a soft spot for Vík and (again) enjoys a great location. Good as a base for exploring the Eyjafjöll mountains (and waterfalls) to the west and then Skaftafell National Park and the Jökulsárlón Glacial Lagoon which are two hours further east. Least birdy place of them all but there is a massive Puffin colony by the village which should be attracting its first birds and there will be wildfowl migration underway in this area. Harlequins on the sea nearby almost certainly. 2-3 hours' drive from Reykjavík.
D) Djúpivogur - A bit of a wildcard as it’s the area I know the least but it’s also one of my favourite areas scenically and it's the furthest from Reykjavík. Fabulous wild coastline in all directions but remote (even though it's on the main ring road) - which may be one of its attractions. Nice wetlands in the village itself and its location means that it is among the first place to get migrants. I've seen strange bedfellows such as Great White Egret and Greenland Gyr Falcon at the same time in the first week of April in this area. 6+ hours’ drive from Reykjavík.
At the risk of provoking the ire of local tourist organisations in Iceland, I wouldn't recommend staying the SW peninsula around Keflavík Airport – this area is usually excellent for birding but is best done on day trips from Reykjavík - the scenery is nothing special and as for the towns...well.
